Question

Tính nhanh:

\(B=\dfrac{1}{1\times4}+\dfrac{1}{4\times7}+\dfrac{1}{7\times10}+...+\dfrac{1}{97\times100}\)

Answer 1

\(B=\dfrac{1}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{97\cdot100}\right)\)

\(=\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)

\(=\dfrac{1}{3}\left(1-\dfrac{1}{100}\right)\)

\(=\dfrac{1}{3}\cdot\dfrac{99}{100}=\dfrac{33}{100}\)

Answer 2

\(3\times B=\dfrac{3}{1\times4}+\dfrac{3}{4\times7}+....+\dfrac{3}{97\times100}\)

\(3\times B=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{100}\)

\(3\times B=1-\dfrac{1}{100}=\dfrac{99}{100}\)

\(B=\dfrac{33}{100}\)

Answer 3

`#ava`

`B` = `frac{1}{1 × 4}` + `frac{1}{4×7}` + `frac{1}{7×10}` + ....+ `frac{1}{97×100}`

`B` = `(``frac{3}{1 × 4}` + `frac{3}{4×7}` + `frac{3}{7×10}` + ....+ `frac{3}{97×100}`)```×1/3`

`B =` `1-1/4+1/4-1/7+1/7-1/10+....+1/97 -1/100) × 1/3`

`B = (1-1/100) × 1/3`

`B= 1/3×99/100`

`B=33/100`