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Solution: Geometric series with alternating signs Evaluate
Chapter 11, Problem 36E(choose chapter or problem)
35-40. Geometric series with alternating signs Evaluate the geometric series or state that it diverges.
\(\sum_{k=1}^{\infty}\left(-\frac{2}{3}\right)^{k}\)
Questions & Answers
QUESTION:
35-40. Geometric series with alternating signs Evaluate the geometric series or state that it diverges.
\(\sum_{k=1}^{\infty}\left(-\frac{2}{3}\right)^{k}\)
ANSWER:Problem 36EGeometric series with alternating signs Evaluate the geometric series or state that it diverges. Answer; Step-1; A sequence ( finite or infinite ) of non zero numbers is called a geometric progression ( abbreviated G.P) iff the ratio of any terms to its preceding term is constant . This non zero constant is usually denoted by ‘r’ and is called common ratio. General term of G.P is = a Thus , if ‘a’ is the first term and ‘r’ is the common ratio , then the G.P is a , ar , a,a………….according as it is finite or infinite.Remarks ; If