Prove the following equality using mathematical induction: For any integer $n \ge 1$
$$\sum_{i=1}^{n} \frac{1}{i(i+1)} = \frac{n}{n+1}$$
I understand for the base base I need to have $n=1$. If I substituted $n$ for 1 and $i$ for 1 I would get
\begin{align} \sum_{i=1}^{1} \frac{1}{1(1+1)} &= \frac{1}{1+1} \\ \sum_{i=1}^{1} \frac{1}{2} &= \frac{1}{2} \end{align}
As for the inductive step, I inputted $n +1$ but it did not work for me because honestly I did not know what to do with the $i$ and what I should do next. How would I go about doing the next step and an explanation for $i$ would be helpful.