先拆項(xiàng)
=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/4-1/10
=3/20
這里的每個(gè)分?jǐn)?shù)都可以拆成兩個(gè)相鄰自然數(shù)的倒數(shù)的差
先拆項(xiàng)=
1/28+1/70+1/130+1/208
=1/(4*7)+1/(7*10)+1/(10*13)+1/(13*16)
=1/3*[(1/4-1/7)+(1/7-1/10)+(1/10-1/13)+(1/13-1/16)]
=1/3*(1/4-1/16)=1/16