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Determine If the Series Converges or Diverges; If the Series n=0(1+4n)5n\sum _ { n = 0 } ^ { \infty } \left( 1 + \frac { 4 } { n } \right) ^ { 5 n }

question 83

Multiple Choice

Determine if the series converges or diverges; if the series converges, find its sum.
- n=0(1+4n) 5n\sum _ { n = 0 } ^ { \infty } \left( 1 + \frac { 4 } { n } \right) ^ { 5 n }


Definitions:

Compounded Monthly

The process of applying interest on both the initial principal and the accumulated interest each month.

Compounded Annually

A method where interest is added to the principal sum at the end of each year, compounding the amount for the next period.

Semi-Annually

Occurring twice a year or every six months, often used in the context of payments or interest calculations.

Ordinary Annuity

A series of equal payments made at regular intervals, with the interest compounding at the end of each period.

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