{an}是等差数列,a1不等于0,Sn是它前n项的和.

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{an}是等差数列,a1不等于0,Sn是它前n项的和.
求lim (n→∞) (Sn+S(n+1))/(Sn+S(n-1))

(Sn+S(n+1))/(Sn+S(n-1))
=[(na1+n(n-1)d/2)+((n+1)a1+n(n+1)d/2)]/[(na1+n(n-1)d/2)+((n-1)a1+(n-1)(n-2)d/2)]
=((2n+1)a1+n^2d)/((2n-1)a1+(n-1)^2d)
所以lim(n趋于无穷)=1

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