If the coefficient of xn2 - n - 182 in x - 1x2 - 2x3 - 3x4 - 4 - xn - n- where n- 8 is k- then k is equal to -

The coefficient of xn^2 +n 182 in (x 1) (x^2 2)......(x^n n) is K , find the value of K , ⇒ the sum of all the term ⇒ n(n+1)2⇒n^ ...

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Standard XII

Mathematics

Greatest Binomial Coefficients

If the coeffi...

Question

If the coefficient of $x^{\frac{n^{2} + n - 18}{2}}$ in $(x - 1) (x^{2} - 2) (x^{3} - 3) (x^{4} - 4) . . . . (x^{n} - n)$ , where $(n \geq 8)$ is $k$ , then $k$ is equal to _______.

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Solution

The coefficient of $x \frac{n^{2} + n - 18}{2}$ in $(x - 1) (x^{2} - 2) . . . . . . (x^{n} - n)$
is $K$ , find the value of $K$ ,
$\Rightarrow$ the sum of all the term
$\Rightarrow \frac{n (n + 1)}{2} \Rightarrow \frac{n^{2} + n}{2}$
$∵$ it $x [\frac{n^{2} + n}{2} - 9] \Rightarrow x [\frac{n^{2} + n - 18}{2}]$
where $(n \geq 8)$ then, the
we have only combination that is $9$
then $K = 9$

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If the coefficient of xn2+n−182 in (x−1)(x2−2)(x3−3)(x4−4)....(xn−n), where (n≥8) is k, then k is equal to _______.

The coefficient of xn2+n−182 in (x−1)(x2−2)......(xn−n)is K, find the value of K,⇒ the sum of all the term⇒ n(n+1)2⇒n2+n2∵ it x[n2+n2−9]⇒x[n2+n−182] where (n≥8) then, thewe have only combination that is 9then K=9

If the coefficient of $x^{\frac{n^{2} + n - 18}{2}}$ in $(x - 1) (x^{2} - 2) (x^{3} - 3) (x^{4} - 4) . . . . (x^{n} - n)$ , where $(n \geq 8)$ is $k$ , then $k$ is equal to _______.