chứng minh rằng 1/6+1/66+1/176+…+1/(5n+1)(5n+6)=n+1/5n+6 27/07/2021 Bởi Brielle chứng minh rằng 1/6+1/66+1/176+…+1/(5n+1)(5n+6)=n+1/5n+6
1/6+1/66+1/176+…+1/(5n+1)(5n+6) = n+1/5n+6 = 1/5 . ( 5/1.6 + 5/6 .11 + 5/11.16 + ….+ 5/(5n+1)(5n+6) =1/5 . (1 − 1/6 + 1/6 − 1/11 + 1/11 − 1/16 +...+ 1/5n+1 − 1/5n+6) = 1/5 . ( 1- 1/5n+6 ) = 1/5 . ( 5n+5/5n+6 ) = n+1/5n+6 (đpcm) Chúc bạn học tốt!Nếu được cho mình xin CTLHN nha! Bình luận
Đáp án: `-` Giải thích các bước giải: `1/6+1/66+1/176+…+1/((5n+1)(5n+6))` `=1/1.6+1/6.11+1/11.16+…+1/((5n+1)(5n+6))` `=1/5(5/1.6+5/6.11+5/11.16+…+5/((5n+1)(5n+6)))` `=1/5(1-1/6+1/6-1/11+1/11-1/16+…+1/(5n+1)-1/(5n+6))` `=1/5(1-1/(5n+6))` `=1/5((5n+6)/(5n+6)-1/(5n+6))` `=1/5*(5n+5)/(5n+6)` `=(n+1)/(5n+6)` Bình luận
1/6+1/66+1/176+…+1/(5n+1)(5n+6) = n+1/5n+6
= 1/5 . ( 5/1.6 + 5/6 .11 + 5/11.16 + ….+ 5/(5n+1)(5n+6)
=1/5 . (1 − 1/6 + 1/6 − 1/11 + 1/11 − 1/16 +...+ 1/5n+1 − 1/5n+6)
= 1/5 . ( 1- 1/5n+6 )
= 1/5 . ( 5n+5/5n+6 )
= n+1/5n+6 (đpcm)
Chúc bạn học tốt!Nếu được cho mình xin CTLHN nha!
Đáp án:
`-`
Giải thích các bước giải:
`1/6+1/66+1/176+…+1/((5n+1)(5n+6))`
`=1/1.6+1/6.11+1/11.16+…+1/((5n+1)(5n+6))`
`=1/5(5/1.6+5/6.11+5/11.16+…+5/((5n+1)(5n+6)))`
`=1/5(1-1/6+1/6-1/11+1/11-1/16+…+1/(5n+1)-1/(5n+6))`
`=1/5(1-1/(5n+6))`
`=1/5((5n+6)/(5n+6)-1/(5n+6))`
`=1/5*(5n+5)/(5n+6)`
`=(n+1)/(5n+6)`