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Statement-1: sum(r =0)^(n) (r +1)""^(n)...

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)`

A

Statement-1 is true, Statement -2 is true, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is true, Statement -2 is true, Statement-2 is not a correct explanation for Statement-1

C

Statement-1 is true, Statement -2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
A
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Stetemet - 1: sum_(r=0)^(n) r. ""^(n)C_(r) = n 2^(n-1) Statement-2: sum_(r=0)^(n) r. ""^(n)C_(r) x^(r) = n (1 + x )^(n-1) x

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Statement-1 : sum_(r=0)^(n) r^(2) ""^(n)C_(r) x^(r) = n (n-1) x^(2) (1 + x)^(n-2) + nx (1 +x)^(n-1) Statement-2: sum_(r=0)^(n) r^(2) ""^(n)C_(r) = n (n-1)2^(n-2)+ n2^(n-1) .