1／1×3+1／2×4+1／3×5+…+1／9×11+1／10×12.有点乱,／是分数分号
问题描述：
1／1×3+1／2×4+1／3×5+…+1／9×11+1／10×12.有点乱,／是分数分号
答
1/[n * (n+2)] = [1/n - 1/(n+2)]/21/(1*3) + 1/(2*4) + 1/(3*5) + ...+ 1/(9*11) + 1/(10*12)= (1/1 - 1/3)/2 + (1/2 - 1/4)/2 + (1/3 - 1/5)/2 + ...+ (1/9 - 1/11)/2 + (1/10 - 1/12)/2= (1/1 - 1/3 + 1/3 - 1/5 ...请问那个（1／2－1／4+1／4…－1／12）÷2是怎么来的？最上面有个公式，裂项公式1/[n * (n+2)] = [1/n - 1/(n+2)]/2