InterviewSolution
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InterviewSolution
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If n is an odd natural number, then `sum_(r=0)^n (-1)^r/(nC_r)` is equal to |
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Answer» Correct Answer - a We have, `sum_(r=0)^(n) ((-1)^(r))/(""^(n)C_(r) )= sum_(r=0)^((n+1)/(2)) {(( -1)^(r))/(""^(n)C_(r) )+ (-1)^(n-r)/(""^(n)C_(n-r))}` `rArr sum_(r=0)^(n) ((-1)^(r))/(""^(n)C_(r) )= sum_(r=0)^((n+1)/(2))(-1)^(r) {(( -1)^(r))/(""^(n)C_(r) )+ (-1)^(n-r)/(""^(n)C_(n-r))}` `rArr sum_(r=0)^(n) ((-1)^(r))/(""^(n)C_(r) )= sum_(r=0)^((n+1)/(2))(-1)^(2) {( 1)/(""^(n)C_(r) )+ (1)/(""^(n)C_(r))}= 0 [{:(therefore " is odd and "),(""^(n)C_(r) = ""^(n)C_(n-r)):}]` . s |
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