
1又2/3+3又14/15+5又34/35+7又62/63+9又98/99+11又142/143?简便方法 急!
1个回答
2014-05-19
展开全部
1又2/3+3又14/15+5又34/35+7又62/63+9又98/99+11又142/143
=(2-1/3)+(4-1/15 )+(6-1/35)+(8-1/63)+(10-1/99)+(12-1/143)
=(2+4+6+8+10+12)-(1/3+1/15+1/35+1/63+1/99+1/143)
=42-(2/3+2/15+2/35+2/63+2/99+2/143)/2
=42-[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)]/2
=42-(1-1/13)/2
=42-6/13
=41又7/13
=(2-1/3)+(4-1/15 )+(6-1/35)+(8-1/63)+(10-1/99)+(12-1/143)
=(2+4+6+8+10+12)-(1/3+1/15+1/35+1/63+1/99+1/143)
=42-(2/3+2/15+2/35+2/63+2/99+2/143)/2
=42-[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)]/2
=42-(1-1/13)/2
=42-6/13
=41又7/13
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