`A=1.4+2.5+3.6+...+99.102`
`A=1(2+2)+2(3+2)+3(4+2)+...+99(100+2)`
`A=1.2+1.2+2.3+2.2+3.4+3.2+...+99.100+99.2`
`A=(1.2+2.3+3.4+...+99.100)+(1.2+2.2+3.2+...+99.2)`
`A=(1.2+2.3+3.4+...+99.100)+2(1+2+3+...+99)`
- Đặt `B=1.2+2.3+3.4+...+99.100`
`C=2(1+2+3...+99)`
- Ta có :
`B=1.2+2.3+3.4+...+99.100`
`=> 3B=1.2.3+2.3.3+3.4.3+...+99.100.3`
`3B=1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)`
`3B=1.2.3+2.3.4-2.3.1+3.4.5-3.4.2+...+99.100.101-99.100.98`
`3B=(2.3.1-1.2.3)+(3.4.2-2.3.4)+(4.5.3-3.4.5)+...+(99.100.98-98.99.100)+99.100.101`
`3B=99.100.101`
`=> B=(99.100.101)/3`
`=> B= 333300`
- Ta lại có :
`C = 2(1+2+3+...+99)`
`C= 2.[(99+1).99:2]`
`C=2.(100.99:2)`
`C=2.(9900:2)`
`C=9900`
`=> A = B + C`
`=> A = 333300+9900`
`=> A=343200`
- Vậy `A=343200`
