= (n+1)².

P(1) is true
Let us assume P(k) is true
= (k+1)².
To prove P(k+1) is true using P(k)
P(k+1) =
= (k+2)²…………(1)
L.H.S of (1)

= (k+1)²
= (k+2)²
Which is the R.H.s of ……………. (1)

P(K+1) is true.
By the Principle of mathematical induction, P(n) is true for all values of n where n N
Hence proved.