1.2 + 2.3 + 3.4 +…. + n(n+1) =

P(1) is true
Let P(k) be true
1.2 + 2.3 + 3.4 +…. + k(k+1) =
To prove P(k+1) to be true using the result of P(k)
1.2 + 2.3 + 3.4 +…. + k(k+1) +(k+1)(k+2)
                                          = ………(1)
L.H.S of (1)
1.2 + 2.3 + 3.4 +…. + k(k+1) +(k+1)(k+2)
                                          = +(k+1) (k+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.