Approximate the Sum to the Indicated Accuracy $\sum _ { n = 1 } ^ { \infty } \frac { 4 ( - 1 ) ^ { n - 1 } } { n ^ { 7 } }$

question 84

Short Answer

Approximate the sum to the indicated accuracy.
$\sum _ { n = 1 } ^ { \infty } \frac { 4 ( - 1 ) ^ { n - 1 } } { n ^ { 7 } }$ (five decimal places)

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Definitions:

Personal Exemptions

A tax deduction allowed by the IRS for oneself and dependents, though it was eliminated for tax years 2018 through 2025 by the Tax Cuts and Jobs Act.

AMT Adjustments

Adjustments required for calculating the Alternative Minimum Tax, an alternative tax system designed to ensure that certain taxpayers pay at least a minimum amount of tax.

Standard Deduction

A fixed dollar amount that reduces the income that is subject to tax and varies according to the taxpayer's filing status.

Taxable Income

The portion of income used to calculate how much tax an individual or a company owes to the government in a given tax year.