How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)(2n+1))+...#?
1 Answer
The nth partial sunm is
The series converge to
Explanation:
Let's perform the partial fraction decomposition of the nth term
The numerators are the same, we compare the denominators
Let
Let
Therefore,
So,
The nth partial sunm is
The series converge to