裂项法,
问题描述：
裂项法,
1,1\3+1\6+1\10+1\15+1\21+1\28+1\36+1\45=?
2,1\3+1\15+1\35+1\63+1\99=?
3,7\8+7\24+7\48+7\80+7\120=?
答
嘿嘿,我来试试
1／3+1／6+1／10+1／15+1／21+1／28+1／36+1／45
=2*(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)
=2*(1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10)
=2*(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)
=2*(1/2-1/10)
=2*2/5
=4/5
1/3+1/15+1/35+1/63+1/99
=1/2×(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11）
＝1/2×(1－1/11)
＝5/11
7/8+7/24+7/48+7/80+7/120
=7/4(1/2+1/6+1/12+1/20+1/30)
=7/4(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6)
=7/4(1-1/6)
=7/4 * 5/6
=35/24