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If sum(r=0)^n(2r+3)/(r+1), Cr=((n+k)*2^(...

If `sum_(r=0)^n(2r+3)/(r+1), C_r=((n+k)*2^(n+1)-1)/(n+1)` then 'k' is

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Statement-1: sum_(r =0)^(n) (r +1)""^(n)C_(r) = (n +2) 2^(n-1) Statement -2: sum_(r =0)^(n) (r+1) ""^(n)C_(r) x^(r) = (1 + x)^(n) + nx (1 + x)^(n-1)

Statement-1: sum_(r =0)^(n) (r +1)""^(n)C_(r) = (n +2) 2^(n-1) Statement -2: sum_(r =0)^(n) (r+1) ""^(n)C_(r) x^(r) = (1 + x)^(n) + nx (1 + x)^(n-1)

Statement-1: sum_(r =0)^(n) (r +1)""^(n)C_(r) = (n +2) 2^(n-1) Statement -2: sum_(r =0)^(n) (r+1) ""^(n)C_(r) x^(r) = (1 + x)^(n) + nx (1 + x)^(n-1)

Prove that sum_(r = 0)^n r^2 . C_r = n (n +1).2^(n-2)

Prove that sum_(r = 0)^n r^2 . C_r = n (n +1).2^(n-2)

sum_(r=0)^n((-1)^r*C_r)/((r+1)(r+2)(r+3))=1/(a(n+b)), then a+b is