Finding the smallest n satisfying $S_n > 10$ Let $S_n = 1 + \frac 12 + \frac 13 + \cdots + \frac 1n$, where $n \in \{ 1,2,3,\cdots\}$ Find the smallest $n$ satisfying $S_n > 10$. 
Sorry, it's my first time asking and I don't know how to format this thing. I still don't see anything even after staring at this for really long. Any clues? 

Should be near 
$$ \lfloor{ \frac{e^9}{2} }+1 $$
I use 
$$ \int_k^{k+1} \frac{1}{t} dt \leq \frac{1}{k} \leq \int_{k-1}^{k} \frac{1}{t} dt $$
You sum and integrate which give you log then you solve for upper and lower bound and verify.
