Question

### Gauthmathier5318

Grade 11 · 2021-01-10

How many terms are needed to estimate f(0.5) to within 0.01?

Good Question (88)

Answer

4.9(347) votes

### Gauthmathier5801

Grade 11 · 2021-01-10

Answer

5 terms.

Explanation

Because f\left(0.5\right) = \sum\limits_{n=1}^{\infty}(-1)^{n+1}\dfrac{(0.5)^n}{\ln(n+1)} satisfies the Alternating Series Test, the error in approximation after n terms is less than the magnitude of the next term. The calculator shows that \dfrac {(0.5)^{n+1}}{\ln (n+2)}<0.01 at n=5 terms.

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