If the limiting sum of the series a +ar + ar^2 +......... is x, then show S_n = [x^n - (x-a)^n]/ x^(n-1) Thanks for any help......
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Originally Posted by anonymous_maths If the limiting sum of the series a +ar + ar^2 +......... is x, then show S_n = [x^n - (x-a)^n]/ x^(n-1) Thanks for any help...... $\displaystyle S_{\infty} = \frac{a}{1 - r} \Rightarrow x = \frac{a}{1-r}$. Re-arrange to make $\displaystyle r$ the subject. Substitute this expression for $\displaystyle r$ into the usual formula for $\displaystyle S_n$ and simplify.
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