Question

1乘以2分之一加2乘以3分之一加3乘以4分之一加…加9乘以10分之一 等于多少?

Answer 1

1乘以2分之一加2乘以3分之一加3乘以4分之一加…加9乘以10分之一 =(1-1/2)+(1-1/3)+(1-1/4)+…+(1+1-1/9)=9-(1/2+1/3+1/4+…+1/10)=9-4861/2520=7+179/2520=6.071

Answer 2

1/(1×2)+1/(2×3)+1/(3×4)+……+1/(9×10)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/8-1/9)+(1/9-1/10)
=1-1/2+1/2-1/3+1/3-1/4+……+1/8-1/9+1/9-1/10
=1-1/10
=9/10