InterviewSolution
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Prove that .^(n)C_(0)- .^(n)C_(1) + .^(n)C_(2)- .^(n)C_(3) + "……" + (-1)^(r) + .^(n)C_(r) + "……" = (-1)^(r ) xx .^(n-1)C_(r ). |
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Answer» Solution :`.^(N)C_(0) - .^(n)C_(1) + .^(n)C_(2) - .^(n)C_(3)+"…"+(-1)^(R ) xx ,^(n)C_(r ) + "…"` Coeffciint of `x^(r )` in `(.^(n)C_(0) - .^(n)C_(1)x + .^(n)C_(2)x^(2) - .^(n)C_(3)x^(3) + "….." + (-1)^(r) xx .^(n)C_(r) + "…..") xx (1+x + x^(2)+x^(3)+"…."+x^(r ) + "....")` `=` Coefficient of `x^(r)` in `(1-x)^(n)(1-x)^(-1)` `=` Coefficient of `x^(r )`in `(1-x)^(n-1)` `= (-1)^(r) xx .^(n-1)C_(r )`. |
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