InterviewSolution
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InterviewSolution
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If `n`is an even positive integer, then find the value of `x`if the greatest term in the expansion of `1+x`^n may have the greatest coefficient also. |
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Answer» Correct Answer - `x gt (n)/(n+2)` and `x lt (n+2)/(n)` If n is even, the greatest coefficient is `.^(n)c_(n//2)`. Therefore, the greatest term is `.^(n)C_(n//2)x^(n//2)`. `:. .^(n)C_(n//2)x^(n//2)gt.^(n)C_((n//2)-1)x^((n-2)//2)` and `.^(n)C_(n//2)x^(n//2) gt .^(n)C_((n//2)+1)x^((n//2)+1)` `rArr (n-n/2+1)/((n)/(2)) xgt 1` and `((n)/(2))/((n)/(2) + 1) x lt 1` `rArr xgt ((n)/(2))/(n/2+1)` and `x lt ((n)/(2)+1)/((n)/(2))` `rArr x ge (n)/(n+2)` and `x lt (n+2)/(n)` |
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