1/3+1/8+1/15+1/24.+1/120=这是六年级考私立中学的题

1/3+1/8+1/15+1/24.+1/120=这是六年级考私立中学的题
1/3+1/8+1/15+1/24.+1/120=
这是六年级考私立中学的题

1/3+1/8+1/15+1/24.+1/120=这是六年级考私立中学的题
原式=1/3＋(1/2)[(1/2－1/4)＋(1/3－1/5)＋(1/4－1/6)＋…＋(1/10－1/12)
=1/3＋(1/2)[(1/2)＋(1/3)－(1/11)－(1/12)]
=175/264

1/3+1/8+1/15+1/24......+1/120= 1/(1*3) + 1/(2*4) + 1/(3*5) + 1/(4*6) + 1/(5*7) + 1/(6*8) + 1/(7*9) + 1/(8*10) + 1/(9*11) + 1/(10*12)
= (1/2)(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8+1/7-1/9+...

全部展开

1/3+1/8+1/15+1/24......+1/120= 1/(1*3) + 1/(2*4) + 1/(3*5) + 1/(4*6) + 1/(5*7) + 1/(6*8) + 1/(7*9) + 1/(8*10) + 1/(9*11) + 1/(10*12)
= (1/2)(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8+1/7-1/9+1/8-1/10+1/9-1/11+1/10-1/12)
= (1/2)(1 + 1/2 - 1/11 - 1/12)
= (1/2)(175/132)
= 175/264

收起

1/（1*3）+1/（2*4）+1/（3*5）+1/（4*6）...+1/（10*12）=1/2*(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6...+1/10-1/12)=1/2*(1+1/2-1/11-1/12)
后面应该就会了吧。