InterviewSolution
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InterviewSolution
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If the number of terms in the expansion of `(1-2/x+4/(x^2))^n , x!=0,`is 28, then the sum of the coefficients ofall the terms in this expansion, is :(1) 64(2) 2187(3) 243(4) 729A. 64B. 2187C. 243D. 729 |
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Answer» Clearly, number of terms in the expansion of `(1 - (2)/(x) + (4)/(x^(2)))^(n)` is `((n + 2)(n + 1))/(2)` or `.^(n + 2)C_(2)` assuming `(1)/(x)` and `(1)/(x^(2))` distinct] `:.((n+2) (n + 1))/(2) = 28` `implies (n + 2) (n + 1) = 56 = (6 + 1) (6 + 1) implies n = 6` Hence, sum of coefficients `= (1 - 2 + 4)^(6) = 3^(6) = 729` Note As `(1)/(x)` and `(1)/(x^(2))` are functions of same variables therefore number of dissimilar terms will be `2n + 1`, i.e., odd, which is not possible, Hence it contains error. |
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