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## Homework Statement

As part of a problem I have to show that [tex]lim_{n\to\infty}\sum_{i=\frac{n}{2}}^{n}\frac{1}{i}=ln(2)[/tex]

## Homework Equations

Taylor expansion of ln(2): [tex]\sum_{i=1}^{\infty}\frac{(-1)^{k+1}}{k}[/tex]

## The Attempt at a Solution

ln(2) can be written as: [tex]ln(2) = \sum_{i=1}^{\frac{n}{2}}\frac{(-1)^{k+1}}{k} + \sum_{i=\frac{n}{2}+1}^{n}\frac{(-1)^{k+1}}{k} + \sum_{i=n+1}^{\infty}\frac{(-1)^{k+1}}{k}[/tex]

Where the middle term looks alot like the sum i need. However I need some way to get rid of the alternating sign change, but i don't see how.