1/3+1/8+1/15+.+1/120,其和等于多少?
问题描述：
1/3+1/8+1/15+.+1/120,其和等于多少?
请老师回答.
答
1/3+1/8+1/15+.+1/120
=1/(1*3)+1/(2*4)+1/(3*5)+……+1/(10*12)
=1/2*[(1/1-1/3)+(1/2-1/4)+(1/3-1/5)+……+(1/10-1/12)]
=1/2*(1+1/2-1/11-1/12)
=1/2*175/132
=175/264