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=?

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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=?
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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...+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...+1/Sn=?
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