Question

1/1×2+1/2×3+1/3×4+1/4×5+……+1/98×99+1/99×100=（）简算

Answer 1

1/1×2+1/2×3+1/3×4+1/4×5+……+1/98×99+1/99×100

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+.+(1/98-1/99)+(1/99-1/100)

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/98-1/99+1/99-1/100

=1-1/100

=99/100