Ta có :
$\frac{1}{2.26}$ + $\frac{1}{2.27}$ + $\frac{1}{3.28}$ + ... + $\frac{1}{100 . 125}$
= $\frac{1}{2.26}$ + ( $\frac{1}{2.27}$ + $\frac{1}{3.28}$ + ... + $\frac{1}{100 . 125}$ ) (1)
Đặt A = $\frac{1}{2.27}$ + $\frac{1}{3.28}$ + ... + $\frac{1}{100 . 125}$
⇒ A = $\frac{25}{25}$ . ( $\frac{1}{2.27}$ + $\frac{1}{3.28}$ + ... + $\frac{1}{100 . 125}$ )
⇒ A = $\frac{1}{25}$ . ( $\frac{25}{2.27}$ + $\frac{25}{3.28}$ + ... + $\frac{25}{100 . 125}$ )
⇒ A = $\frac{1}{25}$ . ( $\frac{1}{2}$ - $\frac{1}{27}$+ $\frac{1}{3}$ - $\frac{1}{28}$+ ... + $\frac{1}{100}$ ) - $\frac{1}{125}$
⇒ A = $\frac{1}{25}$ . ( $\frac{1}{2}$ - $\frac{1}{125}$ ) = $\frac{1}{25}$ . $\frac{123}{250}$ = $\frac{123}{6250}$
Thay A vào (1) ta có :
$\frac{1}{2.26}$ + $\frac{123}{6250}$ = $\frac{1}{52}$ + $\frac{123}{6250}$ = $\frac{7849}{81250}$
