题目
裂项法,
1,13+16+110+115+121+128+136+145=?
2,13+115+135+163+199=?
3,78+724+748+780+7120=?
1,13+16+110+115+121+128+136+145=?
2,13+115+135+163+199=?
3,78+724+748+780+7120=?
提问时间:2020-12-28
答案
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
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
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