Does Series n=1 to infinity 1/2n+1 converge or diverge? I'm thinking it converges, because p would be < 1 right? I'm a little confused.
we know ∑ 1/n diverges
1/(2n+1) is
1/3 1/5 1/7 1/9 ...
1/(2n+1) > 1/(2n+2) = 1/2(n+1)
so ∑1/(2n+1) > ∑1/2(n+1) = 1/2 ∑1/(n+1)
but ∑1/(n+1) is just ∑1/n without the first term.
Similarly, you can show that ∑ 1/(an+b) diverges