Let P(n) = \(\frac1{3.4.5}+\frac2{4.5.6}+\frac3{5.6.7}+....+\frac{n}{(n+2)(n+3)(n+4)}\) \(=\frac{n(n+1)}{6(n+3)(n+4)}\), for all n ∈ N.
Step I:
Step II:
Let us assume that P(n) is true for n = k.
Step III:
We have to prove that P(n) is true for n = k + 1,
i.e., to prove that
Step IV:
From all the steps above, by the principle of mathematical induction, P(n) is true for all n ∈ N.