A geometric series is given by $1+\frac{{{x}^{2}}-5}{4}+\frac{{{\left( {{x}^{2}}-5 \right)}^{2}}}{16

Question

A geometric series is given by $1+\frac{{{x}^{2}}-5}{4}+\frac{{{\left( {{x}^{2}}-5 \right)}^{2}}}{16}+...+\frac{{{\left( {{x}^{2}}-5 \right)}^{n}}}{{{4}^{n}}}+...$ Find the range of values of $x$ such that the series converges. [2] If the ratio of the sum of the first five even-numbered terms to the sum of the first five odd-numbered terms is $\frac{x}{3}$, determine the sum to infinity of the geometric series. [3]

Accepted Answer

(i) $-3< x <-1$ 	ext{ or } $1< x <3$ (ii) $\frac{9}{14}$

2015 CJC Promo Q4 (c)

2015 CJC Promo Q4 (c)

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