chứng minh rằng 1-1/2+1/3-1/4+1/5-…..+1/19-1/20=1/11+1/12+1/13+….+1/20 Giúp mik vs 30/08/2021 Bởi Anna chứng minh rằng 1-1/2+1/3-1/4+1/5-…..+1/19-1/20=1/11+1/12+1/13+….+1/20 Giúp mik vs
`Ta` `có:` `1-1/2+1/3-1/4+1/5-…..+1/19-1/20``=(1+1/2+1/3+1/4+1/5+…+1/19+1/20)-2(1/2+1/4+1/6+…+1/20)``=(1+1/2+1/3+…+1/20)-(1+1/2+1/3+…+1/10)``=1/11+1/12+1/13+…+1/20``Vậy` `1-1/2+1/3-1/4+1/5-…..+1/19-1/20=1/11+1/12+1/13+….+1/20` 100% ko mangj Bài này mk đã từng làm ở đội tuyển rồi nha Bình luận
`1-1/2 +1/3 -1/4 + 1/5-…+1/19 -1/20` `= (1+1/3 + 1/5+…+1/19) – (1/2 +1/4+…+1/20)` `= (1+1/2 + 1/3+1/4+1/5 +…+1/19+1/20) – 2(1/2 + 1/4+…+1/20)` `= 1+1/2 + 1/3+1/4+…+1/20- 1 – 1/2 -…-1/10` `= 1/11 + 1/12 + 1/13 +…+1/20` Bình luận
`Ta` `có:`
`1-1/2+1/3-1/4+1/5-…..+1/19-1/20`
`=(1+1/2+1/3+1/4+1/5+…+1/19+1/20)-2(1/2+1/4+1/6+…+1/20)`
`=(1+1/2+1/3+…+1/20)-(1+1/2+1/3+…+1/10)`
`=1/11+1/12+1/13+…+1/20`
`Vậy` `1-1/2+1/3-1/4+1/5-…..+1/19-1/20=1/11+1/12+1/13+….+1/20`
100% ko mangj
Bài này mk đã từng làm ở đội tuyển rồi nha
`1-1/2 +1/3 -1/4 + 1/5-…+1/19 -1/20`
`= (1+1/3 + 1/5+…+1/19) – (1/2 +1/4+…+1/20)`
`= (1+1/2 + 1/3+1/4+1/5 +…+1/19+1/20) – 2(1/2 + 1/4+…+1/20)`
`= 1+1/2 + 1/3+1/4+…+1/20- 1 – 1/2 -…-1/10`
`= 1/11 + 1/12 + 1/13 +…+1/20`