Resolve into partial fraction :\(\frac{x+4}{\left(x^2-4\right)(x+1)}\)

Resolve into partial fraction \(\frac{x+1}{(x-2)^2(x+3)}\)

Resolve into partial fractions:\(\frac{2x+1}{(x-1)(x^2+1)}\)

A Cricket team of 11 players is to be formed from 16 players including 4 bowlers and 2 wicket-keepers. In how many different ways can a team be formed so that the team contains at least 3 bowlers and at least one wicket-keeper?

By the principle of Mathematical Induction, prove that 1 + 3 + 5 …+ (2n – 1) = n², for all n ∈ N.