How do I write #(5/(1*2))+(5/(2*3))+(5/(3*4))+...+(5/n(n+1))+...#in summation notation, and how can I tell if the series converges?
The given series:
Hence, the given series is converging
Please see some comlementary details below.
I added a few more details
The partial fraction decomposition is
Compare the numerators
The series converges and the limit is