How do you find a formula for the nth partial sum of the series [5/1*2]+[5/2*3]+[5/3*4]+...+[5/n(n+1)]+... and use it to find the series' sum if the series converges?
1 Answer
Feb 28, 2015
First of all we can factor the
This series, except for the factos
Now let's try to separate the term
For the identity principle of polynomials:
So:
That gives:
So:
Let's see now
We can notice now that all the terms except the first and the last will erase themselves, so: