已知数列an中a1=1,前n项和为sn,且P(an,an+1)在直线x-y+1=0上,则1/S1+1/S2+1/S3..
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已知数列an中a1=1,前n项和为sn,且P(an,an+1)在直线x-y+1=0上,则1/S1+1/S2+1/S3...+1/Sn=?
![已知数列an中a1=1,前n项和为sn,且P(an,an+1)在直线x-y+1=0上,则1/S1+1/S2+1/S3..](/uploads/image/z/1225216-64-6.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97an%E4%B8%ADa1%3D1%2C%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BAsn%2C%E4%B8%94P%EF%BC%88an%2Can%2B1%29%E5%9C%A8%E7%9B%B4%E7%BA%BFx-y%2B1%3D0%E4%B8%8A%2C%E5%88%991%2FS1%2B1%2FS2%2B1%2FS3..)
an+1-an=1 a1=1
an=n
sn=n(1+n)/2
1/sn=2/(n+1)n=2(1/n-1/n+1)
原式=2(1-1/2+1/2-1/3+~+1/n-1/n+1)
=2(1-1/n+1)
=2n/n+1
an=n
sn=n(1+n)/2
1/sn=2/(n+1)n=2(1/n-1/n+1)
原式=2(1-1/2+1/2-1/3+~+1/n-1/n+1)
=2(1-1/n+1)
=2n/n+1
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