# Math Help - Binomial coefficients

1. ## Binomial coefficients

Evaluate
$
\sum_{r = 1}^{n}( - 1)^r(1 + \frac {1}{2} + \frac {1}{3} + ...... + \frac {1}{r})\binom{n}{r}
$

where $\binom{n}{r}$ is the binomial coefficient

2. Replace $\binom{n}{r}$ by $\binom{n-1}{r-1}+\binom{n-1}{r}$ and see how the series simplifies