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 \(\frac{5}{2}\)
waec 2020furthermathematics

The correct answer is C. \(\frac{5}{4}\)

(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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