Find the sum of the series
$1+\frac{1}{3^2}+\frac{1.4.1}{1.2.3^4}+\frac{1.4.7.1}{1.2.3.3^6}+...$
I cant guess the general term for this series.But i think this is a type of arithmeticogeometric progression
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The numerator is clearly not obvious. – Zubzub Mar 29 '17 at 17:36
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The denominators are $n!3^{2n}$. – Aravind Mar 29 '17 at 17:36
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You might check if the last 1 is redundant in the numerator, so that they are just $1, 1 \cdot 4, 1 \cdot 4 \cdot 7$, etc. – Aravind Mar 29 '17 at 17:37
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@Aravind, shouldn't the denominator be $(n-1)!3^2n $? – Saksham Mar 29 '17 at 17:41
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I mean to say $3$ to the power $2n$, not $3^2n $ – Saksham Mar 29 '17 at 17:43