Write the general term for the binomial expansion of (a + (x)/(2))^n.

Question

Write the general term for the binomial expansion of (a + (x)/(2))^n.

Asked on April 25, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-04-25T03:31:49.759Z

You're on a roll — Step 1: Write the general term for the binomial expansion of $\left(a + \frac{x}{2}\right)^n$. The general term $T_{r+1}$ is given by: $$ T_{r+1} = \binom{n}{r} a^{n-r} \left(\frac{x}{2}\right)^r $$ $$ T_{r+1} = \binom{n}{r} a^{n-r} \frac{x^r}{2^r} $$ The coefficient of $x^r$ is $\binom{n}{r} a^{n-r} \frac{1}{2^r}$. Step 2: Use the given

Accepted Answer · 2026-04-25T03:31:49.759Z

You're on a roll — Step 1: Write the general term for the binomial expansion of $\left(a + \frac{x}{2}\right)^n$. The general term $T_{r+1}$ is given by: $$ T_{r+1} = \binom{n}{r} a^{n-r} \left(\frac{x}{2}\right)^r $$ $$ T_{r+1} = \binom{n}{r} a^{n-r} \frac{x^r}{2^r} $$ The coefficient of $x^r$ is $\binom{n}{r} a^{n-r} \frac{1}{2^r}$. Step 2: Use the given

Write the general term for the binomial expansion of (a + (x)/(2))^n.