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Geometric series with alternating signs Evaluate the
Chapter 11, Problem 39E(choose chapter or problem)
QUESTION:
35-40. Geometric series with alternating signs Evaluate the geometric series or state that it diverges.
\(\sum_{k=2}^{\infty}(-0.15)^{k}\)
Questions & Answers
QUESTION:
35-40. Geometric series with alternating signs Evaluate the geometric series or state that it diverges.
\(\sum_{k=2}^{\infty}(-0.15)^{k}\)
ANSWER:Problem 39E
Geometric series with alternating signs Evaluate the geometric series or state that it diverges.
Solution
Step 1
In this problem we have to evaluate the geometric series or we have to state that it diverges.
The sum of an infinite Geometric series is given by if .
We have
Here and
Hence the sum ofis
Therefore the sum of the infinite geometric series is