-
MATEMATITG VILLAMTRENNG EGYENES UT AZ EGYETEMRE
1.r. 10001.2.21.3. 1300 '1.4. 388881.5.486t.6.23101.7. 501.t.43r.9. 151.10. 81000r.11. 350r.12. I Ir.13. 961.14.911.15. l46lt. l6.621.17. s9r.18.921.19. 891.20. 381.21. l00lr.22. tnlr.23.01.24. t4r.25.9
a
2.1. l02.2.1602.3.48s2.4.82.5. I I2.6. t52.7.15, mert ez alatt
is ksett egypercet
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ki,rty6&b6l kellkett6
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.
3.1.43.2.53.3. 63.4.73.5.83.6.93.7. l03.8. I I3.9. t23.10. l43.11.203.12. 303.13. 1003.14. 123.15. l53.16. 183.r7.213.r8.243.r9. 303.20.363.2r.423.22.483.23.54
3.24.603.25. 600
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4
4.1.70234.2.711 kilenccel
oszthat64.3. I 154.4.204.5. 584.6. l04.7. 54.8. ' l4.9. 1054.10. 5004.t1.103424.12.20t354.13.102434.14.8994.ls. 9954.16. l0l4.17;3lO I 10+2004.18. 1999994.r9. 900014.20. I4.21. t04.22.454.23.\M4.24.754.25. t45
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s.l. 95.2.75.3. 95.4.85.5.65.6. 1005.7. 1005.8. 19
92 EGEsz 6lts s NTENzfu Ensrrsct vlzseA-EL6Kszfr6 Evrolvnraox
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EGYENES OT AZ EGYETEMRE MATEMATIIG VILLAMTRNING
5.9.215.10. 5s5.11. l85.12.82,2lp-l lq=l5.13.20s.14.3005.15.4200s.16. l05.17.90s.18.275.r9.25.20.445.21.255.22. t255.23. 800s.24.755.25.25
*
6.r .996.2.256.3.26.4. l06.5.3726.6.2t6.7. r826.8.3586.9.40006.10.2r26.11. l06.12. 1086.13.2s6.14. 5006.15. r256.16. 1000006.17.7206.18.66.19. l56.20.96.2r. 126.22.156.23. 186.24.2r6.25.24
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7,t .487.2.607.3.757.4. 10000017.5.97.6. t87.7. I7.8. I7.9.407.10. t47.11. 87.t2.657.13.5s7.r4.757.15. I I I7.16.217.17.607.18. t27.t9.247.20. n27.2t'. t407.22.120007.23.240007.24.67.2s.36
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8.r. t3328.2. t28.3.248.4. 14680008.5. 555600008.6. 88.7.48.8. 168.9. 548.10.278.11.48.12.88.13. l9E.14. l98.r5.458.16.420
8.17. 1688.18.385,
- n(n+l)(2n+l)/68.19. 55, n(n+l/2 ha
n p6ros8.20.9008.21.368.22.848.23.126 "8.24.260.8.25.34
*
9.t .729.2.39.3. ' , t .9.4.299.5. 13
, 9.6.289.7.99.8. 169.9. t99.10. 9549.1t.49.12. s9.13.39.14. l , a 159.15.4, a t2,24,36,
489.16.299.17.3009.1E.2259.19. l99.20. t59.21. 1089.22. t059.23.27e.24. r, (-3)'(-l).19:25.6
j.'
10.1. 310.2. l010.3. 14
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10.4.6, (24-x)12'2 +(24-x)12 ' ll2 +x' l l4:24
10.5. 16r0.6. 30r0.7.910.8. l510.9. 910.10. 1410.11. 210.12. 9, (nem
megold6s9,999... merta tdrtr6sze 0)
10.13. I10.14.7310.15. 9810.16. l510;17.2410.18.4810.19. 9t0.20'.2210.21.710.22.210.23. l l lt0.24.6810.25. l0
*
11.1. 611.2. rr11.3.30r1.4.411.5.5411.6. 3611.7.21611.8. 216r1.9.9611.10. 4011.11. 0tl.l2.211.13. 3tl.l{.211.15. 1211.16. 10
11.17. 511.18. 64tt.rg.711.20.2111.21.01r.22.4211.23.41t.24.2tr.2s.2
*
12.1. 1012.2.912.3.9t2.4. I12.5.3t2.6.412.7.312.8.312.9.212.10.3tz.lr.212.12. I12.t3.43t2.14.2912.15.712.16.2512.17. 6r12.18.812.19.712.20.612.21.212.22.112.23. I12.24.012.25.2
*
13.r. 813.2. 1013.3.413.4.213.5.213.6.3
13.7.413.8.513.9.4t3.10.2413.1r. 40013.12.3213.13.5r3.t4.48413.15.613.16. 913.17.513.18. 3r3.19. l513.20.6113.21.7213.22.1213.23.7213.24.613.25.3
*
14.1. 10814.2.914.3. l014.4. l814.5. 3lt4.6. sr4.7.32r4.8. 102414.9. I14.10.65r4.11. 5514.t2.179414.t3.45214.14. t8214.15.27214.16.72014.17. 414.18.25614.t9.714.20.4t4.21.414.22.914.23.714.24.333
94 reesz gves Es rrurenziv ERErrseer vtzsGA-ELoKESZir6 vrolvRuor
-
14.25.80
{.
15.1. 333515.2.41s.3. 3015.4.615.5. l615.6.815.7.5615.8.2415.9.1215.10.815.11. 615.12.415.13. 3615.t4.415.15.615.16. t215.17.1315.18. l815.19. 1615.20.2715.2t.915.22.1615.23.1415.24. l00l15.25.4
*
16.1. 616.2.616.3. 8t6.4.2016.5. I16.6. 1916.7.616.8.416.9. 816.10. 9r6.tt.6416.12. 1516.13.12
16.14.416.15. l616.16.6416.17.25616.18. l616.19. I16.20.3216.21.6416.22.216.23.6t6.24.6016.25. I
*
17.1.717.2. 517.3. s17.4. 18t7.5.2217.6.817.7.417.8. I17.9.717.10.7t7.tt.617.12.617.13.517.14.917.15. 617.16. 15t7.17.29r7.18. 1217.19.317.20. It7.21.417.22.5t7.23.33017.24.25017.25.0
*
r8.1. l018.2. 3l
18.3. 818.4. 1618.5. r l18.6. 250018.7.31518.8.6118.9.518.10.7812518.11.218.12.418.13.8118.14. I18.15.3218.16. l018.17.618.18. 218.19. 2018.20.4018.21. I l918.22. 18018.23.3118.24.24t8.25.46
*
19.r.2719.2.48t9.3.2819.4.3719.5.79919.6.999r9.7.59998r9.8. tr2419.9. 100019.10. 124819.11.421019.r2.225919.13. 990019.t4.125919.15.971019.16.62rrt9.17.1259r9.18.9521019.19. 102345678919.20.23
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lg.2l.3g I
t9.22.9968t9.23.4919.24.45s19.25.269
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20.r.220.2.420.3. 112620.4.77720.5. l r 1320.6.200420.7. t02320.8.2020.9. 500020.10. l00l20.rt.2820.12. t026920.13. rr7920.14.208820.15.2222r20.16.28820.17. 100001020.18. 102349520.19.14320.20. I I I24.21. ttl20.22. r0220.23.3620.24.25,ll+1420.25.90
*
21.1. 6021.2.25202t.3.321.4.421.5. 88821.6.2222t.7.421.8.63,
32+16+8+4+2+1
21.9.975A+25+12+#3+l
21.10. 500zt.rr.921.12.53321.13.106721.14.421.15.421.16.6021.17.ll221.18.38r6s472902r.r9.9876s4564021.20.421.2r.8334
1e9999/31-leeeeet4l
21.22.833421.23.7s000
900000/3-900000/4
21.24. I2r.25.5
*
22.t .2122.2.022.3.522.4.422.5.522.6.422.7.1822.8.322.9.422.10.622.t1.322.12.422.t3.922.14.622.15.222.16.7622.17.522.t8.622.19.10, minden
primszimraP-l
22.20. I22.21.51222.22.12822.29. tr22.24.5222.25.104
*
23.1. 023.2.723.3.523.4. tl23.s. l323.6.223.7.4123.8.3723.9. 10123.10. 323.tt.423.r2.2323.t3.222223.14.223.15.223.t6.1323.17.323.18. 323.19.3023.20.2923.21. I23.22.223.23.023.24. t0t023.25.31
*
24.1.55524.2.54524.3.7r724.4. t424.5. I 16l I24.6.424.7.524.8.102424.9.400
96 EcEsz evEs Es NTENziv EnEnsot vlzsGA-ELOKEszir6 EvrolvRuor
-
24.rc.224.tt.1224.12.624.13.924.14.5424.15.2024.16.9024.17. t524.18.2224.t9.40024.20.12024.21.024.22.4024.23.324.24,1624.25. l0, aneryzet-
sz6moknak vanpri'ratlan sokoszt6juk
.!.
25.1. I25.2.525.3.2025.4.1225.5.2425.6.6425.7.4825.8. 10525.9. 1225.10. 3025.11.4925.12.425.13. r225.14.225.15.425.16.1125.17.425.18. I25.19.625.20.6225.21. 10025.22.5025.23.t9,(23457
9 1l 13 17 19)
25.24. I25.25. l l I I l11l100
*
26.1. l026.2.19926.3.&826.4.72926.5.026.6.826.7.026.8.226.9. 180
Qt-r).(re-tyz26.10.359
(21-lxl9-lFl26.11.5 mindig
p6ros26.12.626.13.426.14.626.15.426.16.5426.17.40026.18. 6l26.19. 5826.20.980126.21.9826.22.9426.23.326.24.326.25.0
*
27.1.3427.2.327.3.627.4. l027.s.3727.6.lO027.7.527.8.4327.9.8427.r0.72
27.tt.6727.12.7327.r3.49
' 27.14.9127.15.4127.16.6927.17.6527.r8.9327.r9.427.20.3 '27.2r.227.22.3427.23. rO027.24.9927.25.6, l l4, l l4,
U4, tlt2,ll12,Ut2
*
28.1. 928.2.62428.3. 78028.4.25528.5.34028.6.2r028.7. t2628.8. 50028.9.62528.10. 1828.1r.2428.12.19228.13.2s628.14. r9228.15. 828.16. 90028.17. l028.18. l028.19.528.20. l02E.2r.2428.22.185228.23.851228.24. r028.25. s6
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-
t29.r.7229.2.4529.3.36029.4. r2029.5.3029.6. 1529.7.22029.8.24229.9.22229.10.24029.1r. t0629.t2.2529.13.6666029.14. t77629.15.266429.16.33629.17.51229.18. 5629.19. t2029.20.929.21. t029.22.029.23.5629.24.2829.25. 12
.
30.1. 8, FibonacciszAmok
30.2. 1330.3. 830.4. 1330.5. 830.6. 1330.7. t4430.8. 1330:9,23330.10.430.11.2830.12.2, Padovan-
sz6mok30.13. 9
30.14.274Tribonacci-sz6mok
30.15. 930.16.8630.17. l530.18. 5230.19. 14 Catalan
sz6mok30.20. l430.2t. t430.22. t430.23. t430.24. t430.25. 16796
*
31.1.83t.2.731.3. l031.4.931.5.203r.6. 9031.7. l83r.8. 18031.9.30031.10. 300031. i l .9931.t2.3s31.13. 7031.14.831.15. 3596431.16.93t.r7.631.18. l031.19. 531.20. l83r.21.723r.22.443r.2t.5331.24.123r.25.576
*
32.1.232.2. r032.3.2032.4.3532.5.232.6.632.7.532.8. l532.9. t332.10: s32.11. l832.t2. t532.13.2032.14.632.15.832.16.2032.t7.832.18.2032.19.5632.20. n32.21. t232.22.932.23. t732.24. t932.25.6, (0,1,3,4,5
vagy 6).
33.1. 733.2. I I33.3.733.4.2r33.5.2233.6. l933.7.733.8.2233.9.233.10.333.11. 533.12.533.13. 333.14.633.15.433.16. 833.17. l0
98 EGEsz 6ves s NrENzii Enerrsor vESGA-Ea6Gsz.r6 EvFoLyAMoK
-
EcyENEs 0r pa EcvETEMRE MATEMATTKA vru-AurRErurruc
33.18.433.19.833.20. 533.21. l533.22.933.23.2733.24. t633.2s.81ti
34.1. 334.2.3234.3.7034.4. 10834.5.634.6. l834.7.634.8. 334.9.434.10.834.11. 3534.12.4534.13. 6834.14.20034.15. 5, tetomin6k34.16.12, pento-
min6k34.17. I34.18. 1234.19.734.20.634.21.4034.22.034.23. s34.24.234.25.3
a
35.1. l035.2. 1335.3.6'35.4.935.5.235.6. l35.7. l0
a'37.t.3337.2.237.3. 137.4.437.5.737.6.6 ! r37.7.537.8.2037.9.337.10. s37.1r.937.12.3237.13.637.r4. tl37.t5.5237.t6.537.t7.837.18. l I37.r9.737.20. tl37.21. t537.22. t2037,23.6, Nimj6t6k37.24.537.25.30
a
38.1. I38.2.238.3. 338.4.438.5. 338.6. I38.7.038.E.43E.9.238.10. 33t.rr.23t.12. I38.13. 938.14. 038.15. l
35.8. I35.9. 335.10. 335.1r.235.12.435.13. I I35.14.935.15.635.16. 1635.17.635. lE. l035.19. l035.20. 535.21.435.22. t835.23. 835.24. I35.25.4
*
36.r.2036.2. 836.3.436.4.336.s. 836.6.736.7. t336.8. 1436.9. 1436.10.2136.1t.2736.12.736.13.836.14.236.15.2136.16.036.17. 1036.rt. 836.19. s36.20. 836.21.3236.22.836.23.336.24,2036.25.62
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MATEMATIIGVILISMTRENING EGYENES OT AZ EGYETEMRE
38.16. 638.17. I3E.18.438.19.838.20.838.21.838.22.1638.23. 338.24. 5l38.25.50
a
39.1. l939.2. 1339.3. 12039.4. 1939.5.439.6. 15039.7.84, H6ron-
k6Plet39.8. 6039.9. 30039.10. 239.11.1239.12.1339.13. 9639.14. 3939.15.439.16.2039.17.239.18. 7039.19.5039.20. 13539.21.8039.22. I l039.23.3-39.24.439.25.4s
*
40.1.2540.2.2440.3.3240.4.20
40.5.4040.6. 3040.7.4040.8. 7040.9.4940.10. l640.11.640.12.7240.13.27040.14.440.15.340.16. 1440.17.740.18. r40.19. 8040.20.640.21.2440.22.2040.23. r2040.24.14040.25.36
*
4r.1.941.2.3641.3.4441.4.241.5.441.6.741.7. l741.8. 541.9. 1241.10.241.11. l841.12.9641.13.2041.14.441.15. 1941.16. 304t.17.4541.18. 13041.19.9641.20.24041.2r.341.22.7
4r.23.541.24. 194r.25.9
.:.
42.1.842.2.4042.3. l042.4.3 {42.5.10642.6.1242.7.2642.8.1542.9.942.10. 10042.tr.542.12.442.13.442.14.842.15.9042.16.942.17.442.18.942.19.442,20.742.21.3042.22.22542.23.3, hfuomszOg,
nfgyzet,hatsz0g
42.24.l042.25.4
*
43.1. l543.2.3243.3.3443.4.843.5. 1343.6.3443.7.5043.8.2443.9.40043.10. 100
100 ffiet vtzson-er-orszfro EVrouYnuox
-
EcvENES 0r az EGvETEMRE MATEMATTKA vrllAurnEntrqc
43.11. I43.t2.543.13.3643.14.443.15. t043.16.343.17. l043.18. t243.19.443.20.543.21.1343.22.743.23. t443.24. t743.25.0
*
44.1.25u.2.2544.3. t644.4.844.5. I I44.6.5644.7.8444.8. 1344.9.544.10.644.11.2744.t2.12544.13.444.14. t2u.ts. r244.16.1244.17.444.18.244.19. I44.20.244.21.5044.22.10044.23.4144.24.444.25.8
*
45.t .245.2.904s.3. 845.4.2745.5. 17345.6.245.7.445.8.345.9.945.10. 945.11.445.12.745.13.24045.t4.2t045.t5.3245.16.3, szab6lyos
h6romsz0g,n6gyzet,vagyhatszOg
45.17.345.18. l645.19.545.20.445.2t.945.22.16, (32 61e,24
kdtdimenzi6slapja,6s 8hdromdimen-zi6s lapja)
45.23.30(6.s.4/3.2.r).3.2t4
45.24.2445.25.3
*
46.t.4446.2. t8046.3.300346.4.846.5.546.6. 046.7.6046.8.2046.9.3
46.10. 3646.1r. 16046.t2.4046.13.30
-
46.14. t546.15. 1546.16. l046.17.546.18.546.t9.246.20.32, '46.21.446.22.346.23.346.24.446.25.0
.i
47. t .447.2. t447.3.847.4.247.5.247.6.047 .7. 1447.8. t647.9. t447.10.3047.1r.847.12.947.13, t047.14. t847.15.047.16.2447.17.2447.t8.447.19.2847.20.247.21. t2847.22.647.23.6447.24. t647.25.65536
*
DFruDApEsr, A KfrsaFfrg EnErrset AKADM&A, TEL.: 06 (1) 479-0769, [email protected], www.efit,hu 101
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48.1. 8, mdrtani sor48.2.3, m6rtani sor48.3.20, a ktil6nbs6g
sz6mtani sor48.4.21, Fibonacci-
sor48.5.81, Tribonacci-
sor48.6. 110, sz6mok
kettessz6mrend-szerben
48.7.720, faktoridlis48.8. 10395, P6ratlan
sz6mokszorzata
48.9. 15,h6romsztigsz6-mok
48.10.6, {2sz6mjegyei
48.11. 9,n6gyzetsz6mokutols6 jegYei
48.12.lzs,kObsz6mok
48.13. 13,primsz6mok
48.14.29, ikerPrimek(p+2 is prim)
48.15.36, b6velked6sz6mok
48.16.120, szab6lYossokszcigeksztigei
48.17. 13, a 10feli16sakiil0nboz6sz6mrend-szerekben
48.18. 19,n6gYzetmentessz6mok (nincsn6gYzetszilmoszt6juk)
48.19.31, h6nynapb6l 6ll ah6nap nemszdk66vben
48.20.6, h6nykarakterb6l 6lla sz6m leirva
48.21.22, h bettivelkezd6dnek
48.22. 347 , felirhat6ksz6mjegyeik 6salapmiiveletekhaszn6lat6val347:73+4
48.23.20, binomi6lisegyiitthat6k
48.24.28, t0k6letessz6mok
48.25. 8, szab6lYostestekcsricsainakszilma
*
49.1.949.2.2549.3.24349.4. r049.5.349.6.',|49.7.5005049.8.2149.9.200549.10.90149.11.200r49.12.200049.13. l549.14.449.15.849.16.',7349.17.1549.18. 5549.19. 10049.20.l4l549.21.30
49.22.50049.23.289349.24.30149.25.9
*
50.r.202550.2.202550.3. 99150.4. 1050.5. 650.6.850.7.3550.8. 8450.9. 8850.10. 100100150.11. 650.12. 1150.13. 9650.14.72s0.15.216s0.16.6s0.17.3250.18.25s0.19.6650.20.950.21. 1l50.22.250.23.250.24.350.25.5
a
51.1.551.2.051.3.251.4. I51.5. 9
-
51.6. 185r.7.2151.8.2951.9.25s1.10. 051.11. 6
102 ffiTSEct vtzscA-El6rszir6 Evrolvnrrlox
-
EGYENES UT AZ EGYETEMRE MATEMATIKA VILI.AMTRENING
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