1. ## Harmonic series

How can I find N s.t.:
$1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{N}>10$

Thanks

2. The harmonic series diverges very slowly.

By the time you get to a sum of 10, you will have N=12,367

3. Originally Posted by tunaaa
How can I find N s.t.:
$1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{N}>10$
Start by showing that $1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{N} \geqslant \ln(N+1)$.

4. Thanks very much