A = $\frac{1}{1+2}$ + $\frac{1}{1+2+3}$ + ... + $\frac{1}{1+2+..+150}$
A = $\frac{1}{3}$ + $\frac{1}{6}$ + ... + $\frac{1}{150.151:2}$
$\frac{1}{2}$ A = $\frac{1}{6}$ + $\frac{1}{12}$ + ... + $\frac{1}{150.151}$
$\frac{1}{2}$ A = $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + ... + $\frac{1}{150.151}$
$\frac{1}{2}$ A = $\frac{1}{2}$ - $\frac{1}{3}$ + $\frac{1}{3}$ - $\frac{1}{4}$ + ... + $\frac{1}{150}$ - $\frac{1}{151}$
$\frac{1}{2}$ A = $\frac{1}{2}$ - $\frac{1}{151}$ = $\frac{151}{302}$ - $\frac{2}{302}$ = $\frac{149}{302}$
A = $\frac{149}{302}$ . 2 = $\frac{149}{151}$ .
Vậy A = $\frac{149}{151}$.