回复：It is true when n=1; then assume that it is true when n=i and

It is true when n=1; then assume that it is true when n=i and prove that it is true when n=I+1.
Proof:
It is true when n=1: 1 = 1*1
Assuming 1+3+5+...+(2i-1) = i * i (a)
we want to prove
1+3+5+...+(2i-1) + (2i + 1) =( i +1)*( i+1)
Substituting (a) we have
Left = i *i + 2i + 1 = Right