#1:
Are you familiar with telescoping sums?.
Notice what is going on?.
Everything cancels one another and you're left with the 1 in the very beginning. So, it converges to 1.
The others may be similar. Check and see.
For the following series ∑ of a(n) between n=1 and ∞, determine if
the series converges and if so find the limit. (Hint: use partial
fractions to express a(n).)
(a) a(n)=1/(n(n+1))
(b) a(n)=1/(n^2+2n)
(c) a(n)=1/(n(n^2-1))
(As a(1) is not defined consider ∑ of a(n) between n=2 and ∞.)