裂项和公式问题
问题描述：
裂项和公式问题
1/4+1/8+1/12+1/20+1/30=1/2-1/2+1/2-1/4+1/3-1/4+1/4-1/5+1/5-1/6
这个是怎么分解的?
答
1/4+1/8+1/12+1/20+1/30
=(1/4+1/8)+(1/(3*4)+1/(4*5)+1/(5*6))
=((1/2-1/4)+(1/4-1/8))+((1/3-1/4)+(1/4-1/5)+(1/5-1/6))
=(1/2-1/4+1/4-1/8)+(1/3-1/4+1/4-1/5+1/5-1/6)
=(1/2-1/8)+(1/3-1/6)
=3/8+1/6
=26/48
=13/24