Question

奥数题1x2+2x3+3x4+•••+98x99=?

Answer 1

an＝n(n+1)＝n²+n,

∴Sn＝(1²+2²+3²+…+n²)+(1+2+3+…+n)

＝n(n+1)(2n+1)/6+n(n+1)/2

＝n(n+1)(n+2)/3.

∴1×1+2×3+3×4+…+98×99

＝98×99×100÷3

＝485100.