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?
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:
Let's see now
We can notice now that all the terms except the first and the last will erase themselves, so: