Here is the problem: .
Using that is decreasing, then following shows it in one direction.
Now note that:
Also note that if converges that converges.
Can you finish?
i would love if someone could help me with 2 problems im having trouble with.
1) Let , ... be a decreasing sequence of positive numbers. Show that ... converges if and only if ... converges. i saw a similar one on here a couple days ago but this is slightly different
2) Show that a power series has the same radius of convergence as , for any positive integer m