（1）
[sum_{k=1}^n frac{(-1)^k}{k}inom{n}{k}
=sum_{k=1}^n(-1)^kinom{n}{k}int_0^1 x^{k-1} ext{d}x
=-int_0^1sum_{k=1}^n inom{n}{k}(-x)^{k-1} ext{d}x
=int_0^1frac{1-(1-x)^n}{-x} ext{d}x=-int_0^1frac{1-x^n}{1-x}
=-int_0^1sum_{k=1}^n x^{k-1} ext{d}x=-sum_{k=1}^n frac{1}{k}]