Find All Values Of $p$ For Which the Series $\sum _ { n = 1 } ^ { \infty } \frac { \ln \left( n ^ { 9 } \right) } { n ^ { p } }$

question 52

Multiple Choice

Find all values of $p$ for which the series $\sum _ { n = 1 } ^ { \infty } \frac { \ln \left( n ^ { 9 } \right) } { n ^ { p } }$ converges.

• A) \(p < 9\)
• B) \(p < 1\)
• C) \(p > 9\)
• D) \(p > 1\)

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Investment Capital

Funds invested in a business by its owners or shareholders with the expectation of generating a return, used for acquiring assets or financing operations.

Investment Funds

Pooled funds from multiple investors used to collectively invest in securities such as stocks, bonds, and other assets, managed by financial professionals.

Present Value

The value today of a sum of money to be received in the future, after accounting for a certain return rate.

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Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It's the result of reinvesting interest rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.