How do you determine if #a_n=1+3/7+9/49+...+(3/7)^n+...# converge and find the sums when they exist?
Sum to infinity
This is a geometric series:
So we have:
First term is
The sum of a geometric series is given by:
From this we can see that if:
This is a finite value, and the sum is said to converge.
The sum increases without bound, and is said to diverge.