简算 1/3+1/8+1/15+.+1/120
问题描述：
简算 1/3+1/8+1/15+.+1/120
答
1/3+1/8+1/15+...+1/120
=1/(1×3)+1/(2×4)+1/(3×5)+...+1/(10×12)
=(1/2)(1-1/3+1/2-1/4+1/3-1/5+...+1/10-1/12)
=(1/2)[(1+1/2+1/3+...+1/10)-(1/3+1/4+...+1/10+1/11+1/12)]
=(1/2)(1+1/2-1/11-1/12)
=175/264
答
1/3+1/8+1/15+.+1/120
=(1/2)*(1-1/3+1/2-1/4+1/3-1/5+1/4-1/5+.+1/9-1/11+1/10-1/12)
=(1/2)*(1+1/2-1/11-1/12)
=(1/2)*175/132
=175/264