Which one of the following is the greatest coefficient in the...

The general term in the expansion of $(1 + x)^{n}$ is given by $T_{r+1} = ^{n}C_{r} x^{r}$, where the coefficient of $x^{r}$ is ^{n}C_{r}$.<br><br>For an even integer$n$, the greatest binomial coefficient is the middle term, which is ^{n}C_{n/2}$.

Given $n = 100$, which is even, the greatest coefficient is ^{100}C_{100/2} = ^{100}C_{50}$.<br><br>This corresponds to the coefficient of$x^{50}$.<br><br>Answer: The coefficient of$x^{50}