初一的简便计算题3道(1)1/1
(1)1/11*13*15+1/13*15*17+。。。+1/29*31*33
=1/4*(1/11*13-1/13*15)+1/4*(1/13*15-1/15*17)+。。。+1/4*(1/29*30-1/30*31)
=1/4*(1/11*13-1/30*31)=787/531960
(2)1/1*3+1/2*4+1/3*5+。 。。+1/1998*2000
=1/2(1-1/3+1/2-1/4+1/3-1/5+1/4-。。。-1/1998+1/1997-1/1999+1/1998-1/2000)
=1/2(1+1/2-1/1999-1/2000)=5993001/7996000。 ...全部
(1)1/11*13*15+1/13*15*17+。。。+1/29*31*33
=1/4*(1/11*13-1/13*15)+1/4*(1/13*15-1/15*17)+。。。+1/4*(1/29*30-1/30*31)
=1/4*(1/11*13-1/30*31)=787/531960
(2)1/1*3+1/2*4+1/3*5+。
。。+1/1998*2000
=1/2(1-1/3+1/2-1/4+1/3-1/5+1/4-。。。-1/1998+1/1997-1/1999+1/1998-1/2000)
=1/2(1+1/2-1/1999-1/2000)=5993001/7996000。
(3)1/3*7+1/7*11+1/11*15+。。。+1/55*59
=1/4(1/3-1/7+1/7-1/11+。。。+1/55-1/59)
=1/4(1/3--1/59)=14/177。
。收起
