Finding Sum of Alternating Series to Desired Accuracy

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SUMMARY

The discussion focuses on determining the number of terms required to accurately sum the alternating series from n=1 to infinity of the form ((-1)^(n+1))/(n^2) with an error less than 0.0399. The key calculation involves establishing that for the error to be less than 0.0399, the inequality 1/n^2 < 0.0399 must hold. This leads to the conclusion that n must be greater than approximately 5.006, confirming that n=6 is necessary to achieve the desired accuracy.

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  • Understanding of alternating series convergence
  • Familiarity with error estimation in series
  • Basic knowledge of inequalities and algebra
  • Proficiency in mathematical notation and series summation
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  • Study the concept of alternating series and the Alternating Series Test
  • Learn about error bounds in series approximations
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lindsaygilber
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How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

The alternating series from n=1 to infinity of ((-1)^(n+1))/(n^2)
|error| less than 0.0399
i got it down to 1/n^2 is less than 0.0399 but i can't figure out if n = 5 or n=6... please help:(
 
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If you want 1/n2< 0.0399, then you want 1/0.0399= 25.0626< n2 While it is close hat is NOT true for n= 5.
 

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