College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CR: Chapter Review
Problem 35E: Find three positive geometric means between 2 and 8
Related questions
Question
find a formula for the nth partial sum of the series
and use it to determine whether the series converges or diverges. If a
series converges, find its sum.
Expert Solution
Step 1
The formula for the nth partial sum is already given in the question itself:
3/n2 - 3/(n+1)2
Step 2
Let's unfold the series:
n = 1; a1 = 3/12 - 3/22
n = 2; a2 = 3/22 - 3/32
n = 3; a2 = 3/32 - 3/42
and so on.
When we add these terms sequentially to get:
Series, S = a1 + a2 + a3 + ....= 3/12 - 3/22 + 3/22 - 3/32 + 3/32 - 3/42 + .....
Second term cancels the third one, fourth term cancels the fifth one and so on. Only the first term survives.
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