Determine the coefficient of x\(^3\) in the binomial expansion of ( 1 + \(\frac{1}{2}\)x)
- \(\frac{5}{8}\)
- \(\frac{5}{6}\)
-
\(\frac{5}{4}\)
- \(\frac{5}{2}\)
The correct answer is: 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(\(\frac{1}{2} x)^3\) = \(\frac{10}{8} x^3\) =
= \(\frac{5}{4}\)