Tính nhanh:3/2+7/6+13/12+21/20+...+133/132

* Hướng dẫn giải

$\frac{3}{2}$+$\frac{7}{6}$+$\frac{13}{12}$+$\frac{21}{20}$+...+$\frac{133}{132}$
=1+ $\frac{1}{2}$ + 1+ $\frac{1}{6}$+ 1+ $\frac{1}{2}$+ 1+ $\frac{1}{20}$+......+ 1+ $\frac{1}{132}$
=(1+ 1 + 1+.....+ 1) + ( $\frac{1}{2}$+ $\frac{1}{6}$+$\frac{1}{12}$+ $\frac{1}{20}$+....+ $\frac{1}{132}$)
= 11+ ( $\frac{1}{1}$×2+ $\frac{1}{2}$×3+$\frac{1}{3}$×4+$\frac{1}{4}$×5+.....+$\frac{1}{11}$×12)
=11+ ( 1-$\frac{1}{2}$+$\frac{1}{2}$-$\frac{1}{3}$+$\frac{1}{3}$-$\frac{1}{4}$+$\frac{1}{4}$-$\frac{1}{5}$+......+$\frac{1}{11}$-)
=11+(1-$\frac{1}{12}$)
= 11+$\frac{11}{12}$
=$\frac{143}{12}$