An infinite geometric series is given by $\sum\limits_{n=1}^{\infty }{2{{\left( 4-3x \right)}^{n}}}$

Question

An infinite geometric series is given by $\sum\limits_{n=1}^{\infty }{2{{\left( 4-3x \right)}^{n}}}$. Find the range of values of $x$ for which the series has a finite sum.

Accepted Answer

$1 < x < \displaystyle\frac{5}{3}$

2011 NYJC P1 Q2

2011 NYJC P1 Q2

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