How do I find the sum of 1+22+322+423+⋯
I know the sum is ∑∞n=0(n+12n) and the common ratio is (n+2)2(n+1) but i dont know how to continue from here
Answer
After establishing convergence, you could do the following:
S=1+22+322+423+…
⟹12S=12+222+323+424+…
⟹S−12S=1+12+122+123+…
which is probably something you can recognise easily...
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