If this is so, then
therefore
P(n)
P(n+1)
Proof
Express P(n+1) in terms of P(n)
so that if P(n) really is true, then P(n+1) must also be true
(P(n) being true causes P(n+1) to be true).
which, if P(n) is true will equal
Therefore, if the sum is valid for n=1, it's valid for n=2,
if it's valid for n=2, it's valid for n=3,
if it's valid for n=3, then it's valid for n=4
all the way to infinity,
hence if it's valid for n=1, it's valid for all n.
Therefore the equation for the sum of squares is valid