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Determine the coefficient of x\(^3\) in the binomial expansion of ( 1 + \(\frac{1}{2}\)x) 

Further Mathematics
WAEC 2020

Determine the coefficient of x\(^3\) in the binomial expansion of ( 1 + \(\frac{1}{2}\)x) 

  • A. \(\frac{5}{8}\)
  • B. \(\frac{5}{6}\)
  • C. \(\frac{5}{4}\)
  • D. \(\frac{5}{2}\)
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Correct Answer: Option C
Explanation

(1 + \(\frac{1}{2} x )^5\)

1(1)\(^3\)(\(\frac{1}{2} x)^0\) - 5(1)\(^4\)(\(\frac{1}{2} x)^1\)

+ 10 (10)\(^3\)(\(\frac{1}{2} x )^2\) + 10(1)\(^2\) (\(\frac{1}{2} x\))\(^3\) 

Coefficient of x\(^3\) 

10(\(\frac{1}{2} x)^3\) = \(\frac{10}{8} x^3\) =

= \(\frac{5}{4}\) 


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