Well if you know you can avoid induction for the first part, and write it as.

Or if you prefer induction.

assume

then

and i am sure you can finish that off.

the second part can be factored into the product of two consecutive numbers, so it should be fairly obvious that it must be even.

however you have been asked to do it by induction. so

suppose is even for all n up a value k

then is even. now we need to show that if it is still even

replace n with k+1 giving expand it then you add "zero" (i.e add k and then subtract k )

giving

which is even as is even