How do we find the sum of n terms of the following?

Question

Tr= 5^r/[(r+1)(r+2)]

I can see there's an arithmetic progression and a geometric progression?
How do we combine them both to find n terms.

Answer 1

It is neither arithmetic nor geometric. Take a look at the first few terms:

T1 = 5^1/(2*3) = 25/30
T2 = 5^2/(3*4) = 25/12
T3 = 5^3/(4*5) = 25/4
...

As wolframalpha shows, the general sum is not elementary:

http://www.wolframalpha.com/input/?i=sum+(r%3D1..n)+5%5Er%2F%5B(r%2B1)(r%2B2)%5D

Answer 2

I see! Thank you very much!