Problem 1. (4 points) Consider the following infinite series:
sum_(n=1)^(infty ) (1)/(n(n+3))
(a) Find an explicit formula for s_(N), the N-th partial sum of the series.
(b) Find the sum of the infinite series or explain why it does not exist.
Hint. (a) Use partial fractions: express (1)/(n(n+3))=(A)/(n)+(B)/(n+3) for some A and B.
Problem 1. (4 points) Consider the following infinite series:
X
1
n+3
a) Find an explicit formula for sn, the N-th partial sum of the series (b) Find the sum of the infinite series or explain why it does not exist.
1
A
B for some A and B. n+3
Hint. (a) Use partial fractions: express n(n+3)
n
