1/6 + 1/6 x 11 + 1 / 11 x 16 + …+ 1 / n ( n + 5) 02/12/2021 Bởi Charlie 1/6 + 1/6 x 11 + 1 / 11 x 16 + …+ 1 / n ( n + 5)
`1/1.6+1/6.11+1/11.16+…+1/{n(n+5)}` `=1/5(5/1.6+5/6.11+5/11.16+…+5/{n(n+5)})` `=1/5(1-1/6+1/6-1/11+1/11-1/16+…+1/n-1/{n+5})` `=1/5(1-1/{n+5})` `=1/5 . {n+4}/{n+5}` `={n+4}/{5n+25}` Bình luận
Đáp án: Giải thích các bước giải: Ta có : $\dfrac{1}{6}+\dfrac{1}{6.11}+….+\dfrac{1}{n.(n+5)}$ $ = \dfrac{1}{5}.(\dfrac{5}{1.6}+\dfrac{5}{6.11}+…+\dfrac{5}{n.(n+5)})$ $ = \dfrac{1}{5}.(\dfrac{1}{1}-\dfrac{1}{n+5})$ $ = \dfrac{n+4}{5.(n+5)}$ Bình luận
`1/1.6+1/6.11+1/11.16+…+1/{n(n+5)}`
`=1/5(5/1.6+5/6.11+5/11.16+…+5/{n(n+5)})`
`=1/5(1-1/6+1/6-1/11+1/11-1/16+…+1/n-1/{n+5})`
`=1/5(1-1/{n+5})`
`=1/5 . {n+4}/{n+5}`
`={n+4}/{5n+25}`
Đáp án:
Giải thích các bước giải:
Ta có :
$\dfrac{1}{6}+\dfrac{1}{6.11}+….+\dfrac{1}{n.(n+5)}$
$ = \dfrac{1}{5}.(\dfrac{5}{1.6}+\dfrac{5}{6.11}+…+\dfrac{5}{n.(n+5)})$
$ = \dfrac{1}{5}.(\dfrac{1}{1}-\dfrac{1}{n+5})$
$ = \dfrac{n+4}{5.(n+5)}$