Proof by induction $\frac1{1 \cdot 2} + \frac1{2 \cdot 3} + \frac1{3 \cdot 4} + \cdots + \frac1{n \cdot (n+1)} = \frac{n}{n+1}$ Need some help on following induction problem:

$$\dfrac1{1 \cdot 2} + \dfrac1{2 \cdot 3} + \dfrac1{3 \cdot 4} + \cdots + \dfrac1{n \cdot (n+1)} = \dfrac{n}{n+1}$$


Hint:
$$\frac{1}{k(k+1)}= \frac{1}{k} - \frac{1}{k+1}.$$
Hint2:
$$\frac{n}{n+1} = 1 - \frac{1}{n+1}.$$
