InterviewSolution
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The value of sum_(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C_(r ) is |
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Answer» `(1)/(n+1)` `=^(n)C_(r )-(1)/(r+1)*(n!)/(r!(n-r)!)` `=^(n)C_(r )-(1)/(n+1)'^(n+1)C_(r+1)` `:.sum_(r=1)^(n)(-1)^(r-1)(r )/(r+1)*^(n)C_(r )` `=^(n)C_(1)-^(n)C_(2)+C_(3)-.....-(1)/(n+1)['^(n+1)C_(2)-^(n+1)C_(3)+^(n+1)C_(4)-.....]` `=^(n)C_(0)-(1)/(n+1)[-^(n+1)C_(0)+^(n+1)C_(1)]` `=1-(1)/(n+1)[-1+(n+1)]` `=(1)/(n+1)` |
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