Hello,

Question :

Find the sum of the convergent series ( (1/e)^n + ( 1 / n(n+1) ) ) from n=1 to n=infinity

Clearly, the series is a sum of two convergent series

First series is geometric series with sum = a / (1-r) = 1 / ( 1 - (1/e) ) = e / (e-1)

Second series is telescoping series with Sn = 1 - ( 1 / (n+1) ) which approach 1 as n approach infinity

So the sum is the sum of the two series 1 + ( e/(e-1) )

But the book and wolframalpha keep saying that the sum is e/(e-1) !