1／1×3+1／2×4+1／3×5+…+1／9×11+1／10×12.有点乱,／是分数分号

1／1×3+1／2×4+1／3×5+…+1／9×11+1／10×12.有点乱,／是分数分号
1／1×3+1／2×4+1／3×5+…+1／9×11+1／10×12.有点乱,／是分数分号

1／1×3+1／2×4+1／3×5+…+1／9×11+1／10×12.有点乱,／是分数分号
1/[n * (n+2)] = [1/n - 1/(n+2)]/2
1/(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 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11)/2 + (1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + 1/8 - 1/10 + 1/10 - 1/12)/2
= (1 - 1/11)/2 + (1/2 - 1/12)/2
= 5/11 + 5/24
= 175/264