Question

3分之1加上15分之1加上35分之1加上省略号加上2009乘以2011分之1,等于多少

Answer 1

1/(1*3)=(1/1-1/3)*(1/2)

1/(3*5)=(1/3-1/5)*(1/2)

.

1/(2009*2011)=(1/2009-1/2011)*(1/2)

所以1/(1*3)+1/(3*5)+...+1/(2009*2011)=(1/2)*(1/1-1/3+1/3-1/5+...+1/2009-1/2011)

=(1/2)*(1/1-1/2011)

=(1/2)*(2010/2011)

=1005/2011