Question

Bài 1 : Tính hợp lí

1/3+1/6+1/10+1/15+..........+1/45

Answer 1

Lời giải:

$A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+....+\frac{1}{45}$
$\frac{A}{2}=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}$

$=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+....+\frac{1}{9.10}$

$=\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{10-9}{9.10}$

$=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}$

$=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}$

$\Rightarrow A=\frac{4}{5}$