Question
If the sum to infinity of the series $3+5 r+7 r^{2}+\ldots$ is $\frac{49}{9}$, then $r$ is equal to(A) $\frac{1}{4}$(B) $\frac{1}{3}$(C) $\frac{1}{2}$(D) None of these
Step 1
Using sum_{n=0}^∞ r^n = 1/(1-r) and sum_{n=0}^∞ n r^n = r/(1-r)^2 (for |r|<1), S = 2·r/(1-r)^2 + 3/(1-r) = (3 - r)/(1 - r)^2. Set (3 - r)/(1 - r)^2 = 49/9. Show more…
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