- #1

Tremoi

- 1

- 0

## Homework Statement

Does

[itex]\sum_{k=1}^{n}(\frac{1}{2k-1} - \frac{1}{2k}) = \sum_{k=1}^{n}\frac{1}{k + n}[/itex]

hold for [itex]1 \leq n[/itex]

## 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 two sums to each other. I then had an idea about maybe putting each sum on a common denominator and prove that the both denominators and the both numerators are equal but that's not true so I don't really know where to start.

The left terms can be rewritten as [itex]\frac{1}{2k(2k-1)}[/itex] as well but that haven't really helped me either.