Evaluating a finite summation

Question

What is the general formula for the following sum:

$$\sum^N_{n=1}\frac{n+1}{n}$$

where $N$ is a finite natural number.

Answer 1

Note that $\frac{n+1}{n}=1+\frac{1}{n}$ $$\sum_{n=1}^{N}{(1+\frac{1}{n})}=N+H_N$$ where $H_N$ is the N-th harmonic number. Unfortunately there’s no closed form for this sum, just we know that it is asymptotic to $N+\log{N}$