Question 24
Find the sum $$
\begin{aligned} &\frac1{1\cdot3}+\frac1{3\cdot5}+\cdots\\ &\quad+\frac1{(2n-1)(2n+1)}+\cdots\\ &\quad+\frac1{255\cdot257}. \end{aligned}
$$
\begin{aligned} &\frac1{1\cdot3}+\frac1{3\cdot5}+\cdots\\ &\quad+\frac1{(2n-1)(2n+1)}+\cdots\\ &\quad+\frac1{255\cdot257}. \end{aligned}
$$