Find the 3rd term of ≤ft(x/2 - 1)^{8} in descending order of x.

Correct Answer is : 7x6167x^6/16167x6

Find the 3rd term of ≤ft(x/2 - 1)^{8} in descending order of x.

Correct Answer is : 7x6167x^6/16167x6

Test Index

WAEC Further Mathematics 2015 Paper

Question : 5

Total: 40

\left(\frac{x}{2} - 1\right)^{8}

in descending order of x.

$\frac{x^7}{8}$
$\frac{7x^6}{16}$
$\frac{7x^5}{4}$
$\frac{35x^4}{8}$

Validate

Solution:

$\left(\frac{x}{2} - 1\right)^{8} = {}^8C_8\left(\frac{x}{2}\right)^{8}(-1)^0 + {}^8C_7\left(\frac{x}{2}\right)^{7}(-1)^1 + {}^8C_6\left(\frac{x}{2}\right)^{6}(-1)^2 + \dots$

$\text{The third term in the expansion = } {}^8C_6\left(\frac{x}{2}\right)^6(-1)^2$

= $\frac{8!}{6!\,2!}\left(\frac{x^6}{64}\right)(1)$

= $28 \times \frac{x^6}{64} = \frac{7x^6}{16}$

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