Answer
$$
\begin{aligned} \lim _{n \rightarrow \infty} &\left[R\left[\frac{1-(1+i)^{-n}}{i}\right]\right] \\ &=\frac{R}{i} \lim _{n \rightarrow \infty}\left[1-(1+i)^{-n}\right] \\ &=\frac{R}{i}\left[\lim _{n \rightarrow \infty} 1-\lim _{n \rightarrow \infty}(1+i)^{-n}\right] \\ &=\frac{R}{i}[1-0]=\frac{R}{i} \end{aligned}
$$
Work Step by Step
$$
R\left[\frac{1-(1+i)^{-n}}{i}\right]
$$
the limit of this present value equation as n approaches infinity is:
$$
\begin{aligned} \lim _{n \rightarrow \infty} &\left[R\left[\frac{1-(1+i)^{-n}}{i}\right]\right] \\ &=\frac{R}{i} \lim _{n \rightarrow \infty}\left[1-(1+i)^{-n}\right] \\ &=\frac{R}{i}\left[\lim _{n \rightarrow \infty} 1-\lim _{n \rightarrow \infty}(1+i)^{-n}\right] \\ &=\frac{R}{i}[1-0]=\frac{R}{i} \end{aligned}
$$
