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13 4 limits of infinite sequences

Jul 02, 2015

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Education

hisema01

  • 1. Objectives: 1. Find or estimate limits of infinite sequences

2. Investigating Limits Lets take this infinite geometricsequence: t10 0.001 t50 0.000000000000000001 So, since tn is approaching 0 as n getsreally big, we say: 3. Another Example Now, lets look at:tn gets closer andcloser to 1, so we say: 4. Estimating Limits You can often estimate the limit of aninfinite sequence by plugging in large values for n. Example: Find 5. Example Find 6. Theorem If |r| < 1, then 7. Another Method For limits of rational expressions:Look at highest degree term on top and bottom Usually the first termCompare degrees, then use theserules 8. If degrees are equal: limit = ratio of coefficientsExample: 9. If top degree is higher: limit = Example: 10. If bottom degree is higher: limit = 0Example: 11. You Try! 12. The Limit Does Not Exist If the terms do not approach anycertain value, the sequence has no limit. Ex:does not exist 13. You Try! Find the limit of each sequence:1, -4, 9, -16, 25, -36,