`1/6 + 1/30 + 1/70 + 1/126 + ... + 1/966` `\text{THỀ CHO HAY NHẤT}`

Đáp án:

Giải thích các bước giải:

 Đặt `A = 1/6 + 1/30 + 1/70 + 1/126 + .... + 1/966`

`=> 4/2 A = 4/2(1/6+1/30+1/70+1/126+...+1/966)`

`=> 4/2 A = 4/12 + 4/60 + 4/140+ 4/252 + ... + 4/1932`

`=> 2A = 4/(2*6) + 4/(6*10) + 4/(10*14) + 4/(14*18) + ... + 4/(42*46)`

`=> 2A = 1/2-1/6+1/6-1/10+1/10-1/14+1/14-1/18+...+1/42-1/46`

`=> 2A = 1/2 -1/46`

`=> 2A = 11/23`

`=> A = 11/23 : 2`

`=> A = 11/46`

đặt A=$\frac{1}{6}$ +$\frac{1}{30}$+ $\frac{1}{70}$ +...+$\frac{1}{966}$

 $\frac{4}{2}$ A=$\frac{4}{2.6}$ +$\frac{4}{6.10}$+ $\frac{4}{10.14}$+...+ $\frac{4}{42.46}$ 

2A=$\frac{1}{2}$ -$\frac{1}{6}$ +$\frac{1}{6}$ -$\frac{1}{10}$ +$\frac{1}{10}$ -$\frac{1}{14}$ +...+$\frac{1}{42}$ -$\frac{1}{46}$ 

2A=$\frac{1}{2}$ -$\frac{1}{46}$ =$\frac{11}{23}$ 

A=$\frac{11}{23}$ :2 =$\frac{11}{46}$