来自董西广的问题
1/3+1/8+1/15+...
1/3+1/8+1/15+...
1回答
2020-04-26 12:01
1/3+1/8+1/15+...
1/3+1/8+1/15+...
原式=1/(1×3)+1/(2×4)+1/(3×5)+...+1/(18×20)
=1/2×[(1-1/3)+(1/2-1/4)+(1/3-1/5)+...+(1/18-1/20)]
=1/2×(1+1/2-1/19-1/20)
=1/2×(18/19+9/20)
=531/760