Question

Tính nhanh: 1/14+1/14.17+1/17.20+...+1/29.32

Answer 1

Lời giải:$A=\frac{1}{14}+\frac{1}{14.17}+\frac{1}{17.20}+...+\frac{1}{29.32}$

$3A=\frac{3}{14}+\frac{3}{14.17}+\frac{3}{17.20}+...+\frac{3}{29.32}$$3A=\frac{3}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}+...+\frac{1}{29}-\frac{1}{32}$

$=\frac{4}{14}-\frac{1}{32}=\frac{57}{224}$

$\Rightarrow A=\frac{19}{224}$

Answer 2

Lời giải:$A=\frac{1}{14}+\frac{1}{14.17}+\frac{1}{17.20}+...+\frac{1}{29.32}$

$3A=\frac{3}{14}+\frac{3}{14.17}+\frac{3}{17.20}+...+\frac{3}{29.32}$$3A=\frac{3}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}+...+\frac{1}{29}-\frac{1}{32}$

$=\frac{4}{14}-\frac{1}{32}=\frac{57}{224}$

$\Rightarrow A=\frac{19}{224}$