InterviewSolution
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InterviewSolution
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Statement-1: `sum_(r=0)^(n) (1)/(r+1) ""^(n)C_(r) = (1)/((n+1)x) {( 1 + x)^(n+1) -1}^(-1)` Statement-2: ` sum_(r=0)^(n) (""^(n)C_(r))/(r+1) = (2^(n+1))/(n+1)`.A. 1B. 2C. 3D. 4 |
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Answer» Correct Answer - c We have ` sum_(r=0)^(n) (1)/(r+1) ""^(n)C_(r)x^(r)` ` = - (1)/(x(n+1)) sum_(r=0)^(n) (-1)^(r+1) (n+1)/(r+1) ""^(n)C_(r) x^(r+1)` `=- (1)/(x (n+1)) sum_(r=0)^(n) (-1)^(r+1) ""^(n+1)C_(r+1) x^(r +1)` `= - (1)/(x(n+ 1)) {(1-x)^(x+1) -1} - (1)/((n+1) x) {1-(1 - x)^(n+1)}` So, statement-2 is true. Replacing x by 1 in statement-2, we get `sum_(r=0)^(n) (""^(n)C_(r))/(r+1) = (2^(n+1)-1)/(n+1)` So, statement-2 is false. |
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