Question

这个算式有简便方法吗？求求解答

Answer 1

原式=3/2*[ 2/(5*7) +2/(7*9）+.......+2/(11*13)+2/(13*15)]
=3/2*[(1/5 -1/7)+(1/7- 1/9)+.....+(1/11 -1/13)+(1/13-1/15) ]
=3/2*(1/5 -1/15 )
=3/2* 2/15
=1/5

Answer 2

有的
1/n(n+2)=[1/n-1/(n+2)]/2
所以原式=3/2（1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15）
=3/2（1/5-1/15）
=1/5

Answer 3

有
原式=3[1/(5*7)+1/(7*9)+1/(9*11)+1/(11*13)+1/(13*15)]
=3*1/2*(1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=3/2*(1/5-1/15)
=1/5

新年快乐！望采纳，O(∩_∩)O谢谢

Answer 4

原式=3/2*(1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=3/2*(1/5-1/15)
=3/2*2/15
=1/5

Answer 5

有啊……3/(5x7)=3x(1/5-1/7)x1/2=3/2x(1/5-1/7)
同理，3/(7x9)=3/2x(1/7-1/9)
……
最后全部化简，答案是3/2x(1/5-1/15)=1/5