WAEC 2020 · Paper 1 · Q13

Sequences, series & binomial expansion

Determine the coefficient of $x^3$ in the binomial expansion of $\left(1 + \frac{1}{2}x\right)^5$ .

Worked solution (try it first)

The $x^3$ term is $\binom{5}{3}(1)^2\left(\frac{1}{2}x\right)^3$ .
Here $\binom{5}{3} = 10$ and $\left(\frac{1}{2}\right)^3 = \frac{1}{8}$ .
So the coefficient is $10 \times \frac{1}{8} = \frac{5}{4}$ , option C.

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