Homework Statement
Does
\sum_{k=1}^{n}(\frac{1}{2k-1} - \frac{1}{2k}) = \sum_{k=1}^{n}\frac{1}{k + n}
hold for 1 \leq n
Homework Equations
The Attempt at a Solution
It holds for n = 1. I assume that it should be done with induction but I can't find a way actually compare the...