If ''a'' is a convergent serie and limSn=s (x approaches infinite). Is limS(n-1)=s and why?

Question

Does the sum changes in this case and does the limit change too?

Answer 1

In general the limit of the S_n should not change as long as the definition of S_n does not change.

 

By that I mean if S_n = a₁ + ... + a_n and S_n-1 = a₁ + ... + a_n-1 then the limit is the same.

 

 

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