5*9分之1+9*13分之1+13*17分之1+……+101*105分之1=?_数学解答

5*9分之1+9*13分之1+13*17分之1+……+101*105分之1=?

人气：250 ℃　时间：2020-01-27 21:23:16

解答

1/(5*9)+1/(9*13)+...+1/(101*105)
=(1/4)*(1/5-1/9)+(1/4)*(1/9-1/13)+...+(1/4)*(1/101-1/105)
=(1/4)*(1/5)-(1/4)*(1/9)+(1/4)*(1/9)-(1/9)*(1/13)+...+(1/4)*(1/101)-(1/4)*(1/105)
=(1/4)*(1/5)-(1/4)*(1/105)
=(1/4)*(1/5-1/105)
=(1/4)*(20/105)
=1/21