1. Tardigrade
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  4. If f(x)=1+n x+(n(n-1)/2) x2+(n(n-1)(n-2)/6) x3+ ldots ldots+xn Then f11(1)=

Q. If $f(x)=1+n x+\frac{n(n-1)}{2} x^{2}+\frac{n(n-1)(n-2)}{6} x^{3}+\ldots \ldots+x^{n}$ Then $f^{11}(1)=$

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Solution:

$f(x)=1+n x+\frac{n(n-1)}{2} x^{2}+\frac{n(n-1)(n-2)}{6} x^{3}+\cdots .+x^{n}$
$f(x)=(1+x)^{ n }$
$f^{| }(x)=n(1+x)^{ n -1}$
$f^{\| }(x)=n(n-1)(1+x)^{ n -2}$
$f^{\| }(1)=n(n-1) 2^{ n -2}$

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