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已知直线y=[-(n+1)/(n+2)]x+[1/(n+2)](n为正整数)则则S1+S2+S3.S2012=
题目详情
已知直线y=[-(n+1)/(n+2)]x+[1/(n+2)](n为正整数)
则则S1+S2+S3.S2012=_
则则S1+S2+S3.S2012=_
▼优质解答
答案和解析
令x=0
y=1/(n+2)
令y=0
x=1/(n+1)
∴Sn=1/2*1/(n+2)*1/(n+1)
=1/2*1/[(n+1)*(n+2)]
=1/2*[1/(n+1)-1/(n+2)]
裂项求和
S1+S2+S3.S2012
=1/2*(1/2-1/3+1/3-1/4+1/4-1/5+.+1/2012-1/2013+1/2013-1/2014)
=1/2*(1/2-1/2014)
=1/2*1006/2014
=503/2014
y=1/(n+2)
令y=0
x=1/(n+1)
∴Sn=1/2*1/(n+2)*1/(n+1)
=1/2*1/[(n+1)*(n+2)]
=1/2*[1/(n+1)-1/(n+2)]
裂项求和
S1+S2+S3.S2012
=1/2*(1/2-1/3+1/3-1/4+1/4-1/5+.+1/2012-1/2013+1/2013-1/2014)
=1/2*(1/2-1/2014)
=1/2*1006/2014
=503/2014
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