summing series proof

a)prove that if f(r) = r ! then f(r+1) - f(r) = r x r!
b) sum the series 1 x 1! +2 x 2! + 3 x 3! +...+ n x n!

Could someone help me with this.

I haven't learnt how to do this yet but I'm missing the lesson where we will learn about it and I was told to catch it up

thanks