巧算8/(3*3)+16/(15*15)+24/(35*35)+32/(63*63)+40/(99*99)+48/(14
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巧算8/(3*3)+16/(15*15)+24/(35*35)+32/(63*63)+40/(99*99)+48/(143*143)
![巧算8/(3*3)+16/(15*15)+24/(35*35)+32/(63*63)+40/(99*99)+48/(14](/uploads/image/z/7069016-56-6.jpg?t=%E5%B7%A7%E7%AE%978%2F%283%2A3%29%2B16%2F%2815%2A15%29%2B24%2F%2835%2A35%29%2B32%2F%2863%2A63%29%2B40%2F%2899%2A99%29%2B48%2F%2814)
先分析规律
15=3*5,35=5*7,63=7*9,99=9*11,143=11*13
16=5*5-3*3,24=7*7-5*5,32=9*9-7*7,40=11*11-9*9,48=13*13-11*11
再看原题
8/(3*3)=8/9=1-1/9=1-1/3*3
16/(15*15)=16/3*3*5*5=1/3*3-1/5*5
……
48/(143*143)=48/11*11*13*13=1/11*11-1/13*13
所以,
8/(3*3)+16/(15*15)+24/(35*35)+32/(63*63)+40/(99*99)+48/(143*143)
=1-1/3*3+1/3*3-1/5*5+……+1/11*11-1/13*13
=1-1/13*13
=1-1/169
=168/169
15=3*5,35=5*7,63=7*9,99=9*11,143=11*13
16=5*5-3*3,24=7*7-5*5,32=9*9-7*7,40=11*11-9*9,48=13*13-11*11
再看原题
8/(3*3)=8/9=1-1/9=1-1/3*3
16/(15*15)=16/3*3*5*5=1/3*3-1/5*5
……
48/(143*143)=48/11*11*13*13=1/11*11-1/13*13
所以,
8/(3*3)+16/(15*15)+24/(35*35)+32/(63*63)+40/(99*99)+48/(143*143)
=1-1/3*3+1/3*3-1/5*5+……+1/11*11-1/13*13
=1-1/13*13
=1-1/169
=168/169
巧算8/(3*3)+16/(15*15)+24/(35*35)+32/(63*63)+40/(99*99)+48/(14
巧算:8/3/3+16/15/15+24/35/35+32/63/63+40/99/99+48/143/143
有理数题,8/3*3+16/15*15+24/35*35+32/63*63+40/99*99+48/143*143=?
8/3^2+16/15^2+24/35^2+32/63^2+40/99^2+48/143^2等于多少
8/3^2+16/15^2+24/35^2+32/63^2+40/99^2+48/143^2=?
计算8/3²+16/15²+24/35²+32/63²+40/99²+
3、15、35、63、99、【 】、195
3,15,35,63,99的最小公倍数
4/3+16/15+36/35+64/63+100/99
1/3+1/8+1/15+1/24+1/35+1/48+1/63+1/80+1/99怎么求
巧算 /为分数线 1/3+1/15+1/35+1/63+1/99
8-2/3-2/15-2/35-2/63-2/99-2/143-2/195-2/255 巧算