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1/2+1/6+1/12+……+1/4026042请帮个忙好么?
题目详情
1/2+1/6+1/12+……+1/4026042
请帮个忙好么?
请帮个忙好么?
▼优质解答
答案和解析
1/2+1/6+1/12+1/20+1/30+.+1/4026042
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+……+(1/2006-1/2007)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/2006-1/2007
中间抵消
=1-1/2007
=2006/2007
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+……+(1/2006-1/2007)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/2006-1/2007
中间抵消
=1-1/2007
=2006/2007
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