搜搜做题作业网1/6+1/24+1/48/+1/120+1/210+1/336+1/512用简便方法
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：数学作业 时间：2024/07/02 20:22:30
1/6+1/24+1/48/+1/120+1/210+1/336+1/512用简便方法
1/6+1/24+1/60+1/120+1/210+1/336+1/112
=(2/6+2/24+2/60+2/120+2/210+2/336+2/112)*1/2
=(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+1/4*5-
1/5*6+1/5*6-1/6*7+1/6*7-1/7*8+2/112)*1/2
=(1/2-1/7*8+2/112)*1/2
=(1/2-1/56+1/56)
=1/2*1/2
=1/4
=(2/6+2/24+2/60+2/120+2/210+2/336+2/112)*1/2
=(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+1/4*5-
1/5*6+1/5*6-1/6*7+1/6*7-1/7*8+2/112)*1/2
=(1/2-1/7*8+2/112)*1/2
=(1/2-1/56+1/56)
=1/2*1/2
=1/4