Determine If the Series $\sum _ { n = 1 } ^ { \infty } \frac { 2 \cdot 5 \cdot 8 \cdot \ldots \cdot ( 3 n - 1 ) } { 2 ^ { n } n ! }$

question 85

Essay

Determine if the series $\sum _ { n = 1 } ^ { \infty } \frac { 2 \cdot 5 \cdot 8 \cdot \ldots \cdot ( 3 n - 1 ) } { 2 ^ { n } n ! }$ converges or diverges by the Ratio Test or Root Test.

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Definitions:

Stated Interest Rate

The nominal or advertised interest rate on a loan or bond, not accounting for compounding or fees.

Interest Expense

The cost incurred by an entity for borrowed funds, represented as a financial charge for the privilege of borrowing money.

Bond Issuer

The entity, either a company or government, that borrows funds by issuing bonds.

Bond Premium

The additional amount paid over the face value of a bond, reflecting market interest rates lower than the bond's coupon rate.