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katen-ka-za [31]
3 years ago
11

In the expansion of

Mathematics
1 answer:
Mumz [18]3 years ago
5 0

By the binomial theorem, the x^2 term in the expansion of \left(1-\frac x4\right)^n is

\dbinom n21^{n-2}\left(-\dfracx4\right)^2=\dfrac{n!}{2!(n-2)!}\dfrac{x^2}{16}

which suggests that the contribution of the binomial coefficient should make up the remaining factor of 21. That is,

\dfrac{n!}{2!(n-2)!}=\dfrac{n(n-1)}2=21\implies n=7

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