1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2012)的解法
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![1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2012)的解法](/uploads/image/z/4004736-24-6.jpg?t=1%2F%281%2B2%29%2B1%2F%281%2B2%2B3%29%2B1%2F%281%2B2%2B3%2B4%29%2B%E2%80%A6%E2%80%A6%2B1%2F%281%2B2%2B3%2B4%2B%E2%80%A6%E2%80%A6%2B2012%29%E7%9A%84%E8%A7%A3%E6%B3%95)
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2012)的解法
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2012)的解法
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2012)的解法
原式=1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+……+2012)
=2(1/2-1/3)+2(1/3-1/4)+2(1/4-1/5)+.+2(1/2012-1/2013)
=2(1/2-1/3+1/3-1/4+1/3-1/5.+1/2012-1/2013)
=2(1/2-1/2013)
=2011/2013
如满意速采纳
1+2+..+n=(1+n)*n/2
1/(1+2+...+n)=2/n(n+1)=2/n-2/(n+1)
所以:原式=2/2-2/3+2/3-2/4+....+2/2012-2/2013
=2/2-2/2013
=2011/2013再问你一道:已知a b c的大小关系如图所示:---a...
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1+2+..+n=(1+n)*n/2
1/(1+2+...+n)=2/n(n+1)=2/n-2/(n+1)
所以:原式=2/2-2/3+2/3-2/4+....+2/2012-2/2013
=2/2-2/2013
=2011/2013
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