Question

一乘二分之一加二乘三分之一加三乘四分之一........二零一零乘二零一一分之一 这道数学题怎么运算？？

Answer 1

1*1/2+2*1/3+3*1/4+......+2010*1/2011
＝（1-1/2）+（1/2-1/3）+（1/3-1/4）+......+（1/2010-1/2011）
＝1-1/2+1/2-1/3+1/3-1/4+......1/2010-1/2011
＝1-1/2011
＝2010/2011
打字累死了，多给点分吧

Answer 2

1/n(n+1)=1/n-1/(n+1)
1/1×2+1/2×3+.....+1/2010*2011
=1-1/2+1/2-1/3+1/3-1/4+...1/2009-1/2010.+1/2010-1/2011
=1-1/2011
=2010/2011

Answer 3

1/(1*2)+1/(2*3)+1/(3*4)+……+1/(2010*2011)
=(1-1/2)+ (1/2-1/3)+ (1/3-1/4)+……+(1/2010-1/2011)
=1-1/2011
=2010/2011