作业帮1/3+13/15+33/35+61/63+97/99的简便方法
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/04/26 21:25:31
1/3+13/15+33/35+61/63+97/99的简便方法
1/3 +13/15 +33/35 +61/63 +97/99
=(3-2)/3 +(15-2)/15 +(35-2)/35 +(63-2)/63 +(99-2)/99
=5 -(2/3+2/15+2/35+2/63+2/99)
=5-[2/(1×3)+2/(3×5)+2/(5×7)+2/(7×9)+2/(9×11)]
=5-(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=5-(1-1/11)
=5-10/11
=45/11
=(3-2)/3 +(15-2)/15 +(35-2)/35 +(63-2)/63 +(99-2)/99
=5 -(2/3+2/15+2/35+2/63+2/99)
=5-[2/(1×3)+2/(3×5)+2/(5×7)+2/(7×9)+2/(9×11)]
=5-(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=5-(1-1/11)
=5-10/11
=45/11