Determine Whether the Series Converges or Diverges $\sum _ { n = 2 } ^ { \infty } \frac { ( - 1 ) ^ { n } n } { \ln \left( n ^ { 7 } \right) }$

question 20

Short Answer

Determine whether the series converges or diverges. $\sum _ { n = 2 } ^ { \infty } \frac { ( - 1 ) ^ { n } n } { \ln \left( n ^ { 7 } \right) }$

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Definitions:

Compounded Value

Refers to the result of reinvesting the interest or earnings of an investment, causing it to grow exponentially over time.

Annuity Due

An annuity with payments occurring at the beginning of each period.

Amortized Mortgage

A type of loan where the principal and interest are paid down through fixed monthly payments over the loan's term, leading to a fully paid-off mortgage.

Nominal Interest Rate

The interest rate stated on a loan or financial product, not accounting for inflation or fees that affect actual interest earned or paid.