$*$if you please code in java to see how its done$*$

Prove by mathematical induction that for all positive integers $n,$

${\displaystyle \underset{i=1}{\overset{n}{}}}\frac{1}{i(i+1)}=\frac{n}{n+1}$

First, show the base case for this induction. That is$,$ indicate which value of n is the base case, and

show that the formula holds. $(2$ pts$)$

Then state and prove the inductive step. $(4$ pts$)$

Solution: