Hey guys I can't solve the second part of this following question, i.e. 'hence, ...' onwards.

Prove by induction that, for all positive integers n, [(end value=n) (summation notation, sigma) (starting value: r=1)] (r+1)2^r = n[2^(n+1)].

Hence, deduce that [(end value=2n) (summation notation, sigma) (starting value: r=n+1)] [(r+1)2^r + 2^(n+1)] = n[2^(2n+2)].

Sorry it's so messy but I don't have the programs for 'typing math'. Thanks in advance if anybody could help!