Solution Found!
Properties of series Use the properties of
Chapter 10, Problem 10E(choose chapter or problem)
9-14. Properties of series Use the properties of infinite series to evaluate the following series.
\(\sum_{k=1}^{\infty}\left[2\left(\frac{3}{5}\right)^{k}+3\left(\frac{4}{9}\right)^{k}\right]\)
Questions & Answers
QUESTION:
9-14. Properties of series Use the properties of infinite series to evaluate the following series.
\(\sum_{k=1}^{\infty}\left[2\left(\frac{3}{5}\right)^{k}+3\left(\frac{4}{9}\right)^{k}\right]\)
ANSWER:Problem 10EProperties of series Use the properties of infinite series to evaluate the following series. Answer; Step-1 ; Geometric series ; 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 a