Section 5.1 Homework Solutions Write the first four terms of the sequences defined below: 1. k k a k + = 10 , for all integers 1 ≥ k . 3. i i i c 3 ) 1 (− = , for all integers 0 ≥ i . 5. 2 2 ⋅ = n e n , for all integers 0 ≥ n . Compute the first fifteen terms of the following sequence, and give a description in words of its general behavior: 8. n g n 2 log = , for all integers 1 ≥ n . Find explicit formulas for the following sequences: 10. -1, 1, -1, 1, -1, 1, … 11. 0, 1, -2, 3, -4, 5, … 13. , 6 1 5 1 , 5 1 4 1 , 4 1 3 1 , 3 1 2 1 , 2 1 1 − − − − − 16. 3, 6, 12, 24, 48, 96, … Compute the summations and products: 19. = + ∑ = 5 1 ) 1 ( k k 20. = ∏ = 4 2 2 k k
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Section 5.1 Homework Solutions Write the first four terms of the sequences defined below:
1. k
kak +=
10, for all integers 1≥k .
3. i
i
ic3
)1(−= , for all integers 0≥i .
5. 22
⋅
=nen , for all integers 0≥n .
Compute the first fifteen terms of the following sequence, and give a description in words of its general behavior: 8. ngn 2log= , for all integers 1≥n . Find explicit formulas for the following sequences: 10. -1, 1, -1, 1, -1, 1, … 11. 0, 1, -2, 3, -4, 5, …
13. ,61
51,
51
41,
41
31,
31
21,
211 −−−−−
16. 3, 6, 12, 24, 48, 96, … Compute the summations and products:
19. =+∑=
5
1)1(
kk
20. =∏=
4
2
2
k
k
23. =+∑=
1
1)1(
iii
Evaluate the summations and products for the indicated values of the variable.
33. 1;1...31
21
11
2222 =++++ nn
is just 1112 =
35. 3;1
...13
312
211
1=
++
+
+
+
kk
k
41
43
32
21.
133
122
111
=⋅⋅=
+
+
+
Rewrite by separating off the final term.
37. )!1()1()!()!(1
1
1+⋅++= ∑∑
=
+
=
kkiiiik
i
k
i
39. ∑∑=
+
=
+⋅+++=+n
m
n
mnnmmmm
1
1
1)2()1()1()1(
Write each of the following using summation or product notation: 43. =+−+−+− 2222222 7654321