Find the set of values of $x$ for which the series $\underset{n=1}{\overset{\infty }{\mathop \sum }}

Question

Find the set of values of $x$ for which the series $\underset{n=1}{\overset{\infty }{\mathop \sum }}\,{{\left( \frac{2x}{x+1} \right)}^{n}}$ has a finite sum. [4] Hence, find the sum in terms of $x$. [2]

Accepted Answer

$S_\infty = \frac{2x}{1-x}$

Sigma Notation Q2

Sigma Notation Q2

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