$\frac{1}{1×3}$ + $\frac{1}{3×5}$ + $\frac{1}{5×7}$ +...+ $\frac{1}{23×25}$ + $\frac{1}{25×27}$
= $\frac{1}{2}$ × ($\frac{2}{1×3}$ + $\frac{2}{3×5}$ + $\frac{2}{5×7}$ +...+ $\frac{2}{23×25}$ + $\frac{2}{25×27}$)
= $\frac{1}{2}$ × (1 - $\frac{1}{3}$ + $\frac{1}{3}$ - $\frac{1}{5}$ + $\frac{1}{5}$ - $\frac{1}{7}$ +...+ $\frac{1}{23}$ - $\frac{1}{25}$ + $\frac{1}{25}$ - $\frac{1}{27}$)
= $\frac{1}{2}$ × (1 - $\frac{1}{27}$
= $\frac{1}{2}$ × ($\frac{27}{27}$ - $\frac{1}{27}$)
= $\frac{1}{2}$ × $\frac{26}{27}$
= $\frac{13}{27}$
