1/(12*13)+1/(13*14)+1/(14*15)+1/(15*16)+1/(16*17)+1/(17*18)+1/(18*19)+1/(19*20)=?
来源:百度知道 编辑:UC知道 时间:2024/06/05 01:11:20
简便算法,详细步骤!
1/a(a+1)=1/a-1/(a+1)
1/(12*13)+1/(13*14)+1/(14*15)+1/(15*16)+1/(16*17)+1/(17*18)+1/(18*19)+1/(19*20)
=1/12-1/13+1/13-1/14+1/14-1/15+……+1/19-1/12
=1/12-1/20
=5/60-3/60
=2/60
=1/15
=(1/12-1/13)+(1/13-1/14)+...+(1/19-1/20)
=1/12-1/20
=1/30
原式=(13-12)/12*13+(14-13)13*14+——-----
=13/12*13-12/12*13+。。。。。。
=1/12-1/13+。。。。。。。+1/19-1/20
=1/12-1/20
=(5-3)/60
=1/30
化简=1/12-1/13+1/13-1/14+1/14-1/15+..........1/18-1/19+1/19-1/20=1/12-1/20=1/30
1/11+1/12+1/13+1/14+1/15=?
1/12*13+1/13*14+.......+1/19*20
比较大小:1/11+1/29 1/12+1/25 1/13+1/21 1/14+1/19
1/(12×13)+1/(13×14)+1/(14×15)。。。+1/(19×20)=?
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已知1-1/2=1/2 1/2-1/3=1/6 1/3-1/4=1/12 那么1/6-1/7=()1/12-1/13=()1/2+1/6+1/12=()
7/12-9/20+1/30-13/40+15/56=?
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1/1*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+1/10*11+1/11*12+1/12*13+1/13*14+1/14*15=?