Question

### Gauthmathier8844

Grade 12 · 2021-01-10

If the sum of the alternating series \sum\limits _{n=1}^{\infty }\dfrac {(-1)^{n-1}}{2n-1} is approximated by s_{50}, find the maximum absolute error.

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Answer

5(982) votes

### Gauthmathier5546

Grade 12 · 2021-01-10

Answer

0.0099

Explanation

For the alternating series \sum\limits _{n=1}^{\infty }\dfrac {(-1)^{n-1}}{2n-1} approximated by s_{50}, the maximum absolute error |R_{n}|< a_{n+1}, so |R_{50}|< a_{51}=\dfrac{\left(-1\right)^{50}}{101}=\dfrac {1}{101}\approx 0.0099.

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