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Q 43.

Expert-verifiedFound in: Page 615

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

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

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.

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