InterviewSolution
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If (x+1/x+1)^(6)=a_(0)+(a_(1)x+(b_(i))/(x))+(a_(2)x^(2)+(b_(2))/(x^(2)))+"...."+(a_(6)x^(6)+(b_(6))/(x^(6))), then |
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Answer» `a_() = 141` (1) `a_(0) = 1 +.^(6)C_(2)..^(2)C_(1) + .^(6)C_(4)+.^(4)C_(2)+.^(6)C_(6).^(6)C_(3)` `= 1+30+90+20 = 141` (2) `a_(5) = .^(6)C_(5) xx` Coefficient of `x^(5)` in `(x+1/x)^(5)` `= .^(6)C_(5).^(5)C_(0) = 6` (3) Putting , `x = 1` `a_(0) + (a_(1) + b_(1)) + (a_(2)+b_(2))= 3^(6)` `:. underset(i=1)overset(6)sum(a_(i)+b_(i)) = 3^(6) - 141 = 588` |
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