Well if you know you can avoid induction for the first part, and write it as.
Or if you prefer induction.
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 )
which is even as is even