Question

determine if convergent/divergent, if convergent find its sum
series from n =1 to n = inf
of 1/e^n + 1/(n(n+1))
i know i can break this into two series, 1/e^n = (1/e)^n which is a convergent geometric series
but im a bit braindead and cannot think of a way to show that the other part is also convergent

Answer 1

1/(n^2 +n)
i guess i could use the DCT to compare this to 1/n^2 which converges by p-series and therefore it also converges

Answer 2

yeah

Answer 3

tnx

Answer 4

np

Answer 5

i know how to determine the sum for the g.s one but what about this 2nd series? how would i determine its sum

Answer 6

hold on plz