If `(1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + … + C_(n) x^(n)`,
Show that `(2^(2))/(1*2) C_(0) + (2^(3))/(2*3) C_(1) + (2^(4))/(3*4)C_(2) + ...+ (2^(n+2)C_n)/((n+1)(n+2))= (3^(n+2)-2n-5)/((n+1)(n+2))`

Explanation

To solve the problem, we start with the binomial expansion of \((1 + x)^n\):

\[ (1 + x)^n = C_0 + C_1 x + C_2 x^2 + \ldots + C_n x^n \]

where \(C_k = \binom{n}{k}\) are the binomial coefficients. We need to show that:

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