Friday, April 22, 2016

calculus - Sum of infinite series 1+frac22+frac322+frac423+cdots





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+

S12S=1+12+122+123+

which is probably something you can recognise easily...


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