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.

\(\frac{5}{2}\)

Correct answer is C

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

= \(\frac{5}{4}\)