计算1/4+1/12+1/24+1/40+···+1/180,过程也写一下、教教

题目

计算1/4+1/12+1/24+1/40+···+1/180,过程也写一下、教教

答案

1/2=1-1/2,1/6=1/(2*3)=1/2-1/3,1/12=1/(3*4)=1/3-1/4.
1/4+1/12+1/24+1/40+···+1/180
=1/2*(1/2+1/6+1/12+1/20+.+1/90)
=1/2*(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/9-1/10)
=1/2*(1-1/10)
=1/2*9/10
=9/20