I need help with these four questions (If possible, can it be explained in steps):

1.

Work out $\displaystyle \displaystyle\sum_{r=n}^{2n}\frac{r^2}{1}$

2.

Given that $\displaystyle f(r) \equiv 1 \frac{1}{r(r+1)}$, show that $\displaystyle f(r) - f(r+1) \equiv \frac{2}{r(r+1)(r+2)}$

3.

Prove that $\displaystyle \displaystyle\sum_{r=1}^{n}\frac{1}{(r+1)(r+2)}= \frac{n}{2(n+2)}$

4.

Find the sum of the series $\displaystyle 1^2 - 2^2 + 3^2 - 4^2 + ... - (2n)^2$