Estimate the magnitude of the error involved in using the sum of the first two terms to approximate the sum of the entire series summation from n equals 1 to infinity left parenthesis negative 1 right parenthesis superscript n plus 1 baseline startfraction left parenthesis 0.08 right parenthesis superscript n over n endfraction

the magnitude of the error is 2.9959 × 10⁻⁹

Step-by-step explanation:

By Alternating series estimation theorem

is satisfies

(i) for all n

(ii)

The formula for magnitude of error is

Let

We can see

For all n ∈ N

That means for all   n ∈ N

The alternating series estimation theorem is

After stop adding the term with n = 6

the series tells that the error is smaller than the term with a

Therefore

the magnitude of the error is 2.9959 × 10⁻⁹

594 square inches

step-by-step explanation:

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