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Geometric series with alternating signs
Chapter 11, Problem 37E(choose chapter or problem)
35-40. Geometric series with alternating signs Evaluate the geometric series or state that it diverges.
\(3 \sum_{k=0}^{\infty} \frac{(-1)^{k}}{\pi^{k}}\)
Questions & Answers
QUESTION:
35-40. Geometric series with alternating signs Evaluate the geometric series or state that it diverges.
\(3 \sum_{k=0}^{\infty} \frac{(-1)^{k}}{\pi^{k}}\)
ANSWER:Problem 37EGeometric 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 the last term