The largest term in the expansion of $\left(\frac{b}{2} + \frac{b}{2}\right)^{100}$ is ;

Given $\left(\frac{b}{2}+\frac{b}{2}\right)^{100}$

The largest term will be the middle term In this expansion, the middle term is $51^{\text {st }}$ term

$\begin{aligned} \therefore r & =50 \\ T_{r+1} & ={ }_{c_{c_{r}}} x^{n-r} y^{r} \\ T_{50+1} & ={ }^{100}{ }_{c_{50}}\left(\frac{b}{2}\right)^{100-50}\left(\frac{b}{2}\right)^{50} \\ & ={ }^{100} c_{50}\left(\frac{b}{2}\right)^{100} \end{aligned}$

$\therefore$ The largest term in expansion of $\left(\frac{b}{2}+\frac{b}{2}\right)^{100}$ is ${ }^{100} c_{50}\left(\frac{b}{2}\right)^{100}$