Question

1×3+2×4+3×5+.+99×101奥数题怎么写

Answer 1

1×3+2×4+3×5+.+99×101

=(2-1)(2+1)+(3-1)(3-1)+(4-1)(4+1)+.+(100-1)(100+1)

=2^2-1+3^2-1+4^2-1+.+100^2-1

=1^2+2^2+3^2+.+100^2-1x100

=100(100+1)(200+1)/6-100

=338250

注：常用公式1^2+2^2+3^2+4^2+5^2………………+n^2=n(n+1)(2n+1)/6