A = $\frac{9}{1.2}$ + $\frac{9}{2.3}$ + $\frac{9}{3.4}$ + ... + $\frac{9}{99.100}$
⇒ $\frac{1}{9}$A = $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + ... + $\frac{1}{99.100}$
= 1 - $\frac{1}{2}$ + $\frac{1}{2}$ - $\frac{1}{3}$ + $\frac{1}{3}$ - $\frac{1}{4}$ + ... + $\frac{1}{99}$ - $\frac{1}{100}$
= 1 - $\frac{1}{100}$
= $\frac{100}{100}$ - $\frac{1}{100}$
= $\frac{99}{100}$
⇒ A = $\frac{1}{9}$ . $\frac{99}{100}$ = $\frac{11}{100}$
Vậy A = $\frac{11}{100}$.
HỌC TỐT!
