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Expert-verified Found in: Page 615 ### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861 # Given that ${a}_{0}=-3,{a}_{1}=5,{a}_{2}=-4,{a}_{3}=2$ and $\underset{k=2}{\overset{\infty }{\sum {a}_{k}}}=7$, find the value of $\underset{k=0}{\overset{\infty }{\sum {a}_{k}}}$.

The value of $\underset{k=0}{\overset{\infty }{\sum {a}_{k}}}=9$.

See the step by step solution

## Step 1. Given information.

Given that ${a}_{0}=-3,{a}_{1}=5,{a}_{2}=-4,{a}_{3}=2$ and $\underset{k=2}{\overset{\infty }{\sum {a}_{k}}}=7$.

## Step 2. Express the series in terms of known values.

Value of $\underset{k=0}{\overset{\infty }{\sum {a}_{k}}}$ can be obtained as follows.

$\begin{array}{rcl}\underset{k=0}{\overset{\infty }{\sum {a}_{k}}}& =& {a}_{0}+{a}_{1}+\underset{k=2}{\overset{\infty }{\sum {a}_{k}}}\\ & =& -3+5+7\\ & =& 9\end{array}$

Therefore, value of $\sum _{k=0}^{\infty }{a}_{k}$ is 9. ### Want to see more solutions like these? 