Question 856463
step1 check {{{P[1]}}}
{{{S[1]=1^2=1}}} (so true for first case)

step2 check that {{{P[k]}}} implies {{{P[k+1]}}}
in this case...
{{{S[n] + a[n+1] = S[n+1]}}}

{{{n^2+2n+1=(n+1)}}}

true so we are done (it must be true for all n)