The Alternating Series Error Estimate

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  • #1
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summation from 1 to infinite: (5n)/(n^2+1)
What is the maximum amount of error of s4 as compared to the infinite series?

error=S-Sn<bn+1



I got S4=-14/17
and S5=-25/26
but how you suppose to get S? i though you can't tell what a alternating series converge to
 

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  • #2
HallsofIvy
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The key point about an "alternating series", with decreasing terms, is that the sum up to [itex]a_n[/itex] lies between the sum up to [itex]a_{n-1}[/itex] and the sum up to [itex]a_{n-2}[/itex]. And, therefore, the actual sum lies between any two consective partial sums. That is, the entire sum lies between [itex]S_4[/itex] and [itex]S_3[/itex] so the error cannot be larger than the distance between those two.
 

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