\(\left(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{98.99.100}\right)x=-3\)
\(\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{98.99}-\dfrac{1}{99.100}\right)x=-3\)
\(\dfrac{1}{2}.\left(\dfrac{1}{2}-\dfrac{1}{9900}\right)x=-3\)
\(\dfrac{1}{2}.\dfrac{4949}{9900}x=-3\)
\(\dfrac{4949}{19800}x=-3\)
\(x=-3:\dfrac{4949}{19800}\)
\(x=-\dfrac{59400}{4949}\)
`(1/[1.2.3]+1/[2.3.4]+....+1/[98.99.100]).x=-3`
`1/2.(2/[1.2.3]+2/[2.3.4]+....+2/[98.99.100]).x=-3`
`(1/[1.2]-1/[2.3]+1/[2.3]-1/[3.4]+....+1/[98.99]-1/[99.100]).x=-3:1/2`
`(1/[1.2]-1/[99.100]).x=-6`
`(1/2-1/9900).x=-6`
` 4949/9900 . x=-6`
`x=-6:4949/9900=-59400/4949`