Bài 5:
`A=3/(1.5)+3/(5.9)+3/(9.13)+...+3/(61.65)`
`=3/4 .(4/(1.5)+4/(5.9)+4/(9.13)+...+4/(61.65))`
`=3/4 .(1-1/5+1/5-1/9+1/9-1/13+...+1/61-1/65)`
`=3/4 .(1-1/65)`
`=3/4 .(65/65-1/65)`
`=3/4 . 64/65`
`=48/65`
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Ta có:`1+2+3+4+...+2021=(2021+1)/2 .2021=1011.2021`
`B=1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+4+...+2021)`
`=1/3+1/6+1/10+...+1/(1011.2021)`
`=2/6+2/12+2/20+...+2/(2021.2022)`
`=2.(1/(2.3)+1/(3.4)+1/(4.5)+...+1/(2011.2022))`
`=2.(1/2-1/3+1/3-1/4+1/4-1/5+...+1/2011-1/2022)`
`=2.(1/2-1/2022)`
`=2.(1011/2022-1/2022)`
`=2. 1000/2022`
`=1000/1011`
Bài 6:
`(2x-1)+(4x-2)+(6x-3)+...+(400x-200)=5+10+15+...+1000`
-Số số hạng:`(1000-5):5+1=200(số)`
-Tổng:`(1000+5).200:2=100 500`
`→(2x-1)+2(2x-1)+3(2x-1)+...+200(2x-1)=100 500`
`→(2x-1)(1+2+3+...+200)=100 500`
-Số số hạng:`(200-1):1+1=200(số)`
-Tổng:`(200+1).200:2=20 100`
`→(2x-1).20 100=100 500`
`→2x-1=100 500:20 100`
`→2x-1=5`
`→2x=5+1`
`→2x=6`
`→x=6:2`
`→x=3`
