Question

1x2+2x3+3x4+4x5+...……+99x100

Answer 1

`A=1.2+2.3+3.4+4.5+...+99.100`

`3A= 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3+ … + 99.100.3`
`3A= 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)`
`3A= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100`
`3A = 99.100.101`
`A = (99.100.101)/3`
`A = 333 300`