Question
If $\sum_{n=1}^{\infty} x^{n-1}=a$ and $\sum_{n=1}^{\infty} y^{n-1}=b$ where $|x|,|y|<1$,then $\sum_{n=1}^{\infty}(x y)^{n-1}=$(A) $a b$(B) $\frac{a+b-1}{a b}$(C) $\frac{1}{1-a b}$(D) $\frac{a b}{a+b-1}$
Step 1
Here, the common ratios are $x$ and $y$ for the two series given in the question. So, we have: \[a = \frac{1}{1-x}\] \[b = \frac{1}{1-y}\] Show more…
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