`A=1.3+2.4+3.5+4.6+...+20.22`
`=> A=1.(2+1)+2.(3+1)+3.(4+1)+4.(5+1)+...+20.(21+1)`
`=> A=1.2+1+2.3+2+3.4+3+4.5+4+...+20.21+20`
`=> A=(1.2+2.3+3.4+...+20.21)+(1+2+3+4+...+20)`
- Đặt `B=1.2+2.3+3.4+4.5+...+20.21`
`C=1+2+3+4+...+20`
- Ta có :
`B=1.2+2.3+3.4+4.5+...+20.21`
`=> 3B=1.2.3+2.3.3+3.4.3+4.5.3+...+20.21.3`
`=> 3B=1.2.3+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+20.21.(22-19)`
`=> 3B=1.2.3+2.3.4-2.3.1+3.4.5-3.4.2+4.5.6-4.5.3+...+20.21.22-20.21.19`
`=> 3B=(1.2.3-2.3.1)+(2.3.4-3.4.2)+(3.4.5-4.5.3)+...+(19.20.21-20.21.19)+20.21.22`
`=> 3B=20.21.22`
`=> B=(20.21.22)/3`
`=> B=3080`
___________________________
`C=1+2+3+4+...+20`
`=> C=(20+1).20:2`
`=> C=21.20:2`
`=> C=210`
- Ta lại có :
`A=B+C`
`=> A=3080+210`
`=> A=3290`
