`A=1/(1×2×3)+1/(2×3×4)+...+1/(98×99×100)`
`⇒A=1/2×(2/(1×2×3)+2/(2×3×4)+...+2/(98×99×100))`
`⇒A=1/2×(1/(1×2)-1/(2×3)+1/(2×3)-1/(3×4)+...+1/(98×99)-1/(99×100))`
`⇒A=1/2×(1/(1×2)-1/(99×100))`
`⇒A=1/2×(1/2-1/9900)`
`⇒A=1/2×(4950/9900-1/9900)`
`⇒A=1/2×4949/9900`
`⇒A=4949/19800`