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Answer: Geometric series with alternating signs Evaluate
Chapter 11, Problem 40E(choose chapter or problem)
QUESTION:
35-40. Geometric series with alternating signs Evaluate the geometric series or state that it diverges.
\(\sum_{k=1}^{\infty} 3\left(-\frac{1}{8}\right)^{3 k}\)
Questions & Answers
QUESTION:
35-40. Geometric series with alternating signs Evaluate the geometric series or state that it diverges.
\(\sum_{k=1}^{\infty} 3\left(-\frac{1}{8}\right)^{3 k}\)
ANSWER:Problem 40EGeometric series with alternating signs Evaluate the geometric series or state that it diverges. SolutionStep 1In 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 ofisTherefore the sum of the infinite geometric series is