fiNd a Closed Form for the Generating Function for the Sequence

question 108

Short Answer

find a closed form for the generating function for the sequence.
- $$\left( \begin{array} { c } 50 \\1\end{array} \right) , 2 \left( \begin{array} { c } 50 \\2\end{array} \right) , 3 \left( \begin{array} { c } 50 \\3\end{array} \right) , \ldots , 50 \left( \begin{array} { c } 50 \\50\end{array} \right) , 0,0,0 , \ldots$$

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Definitions:

Semi-Annually Compounded

A rephrasing of "compounded semi-annually," where interest is calculated twice a year on the initial principal and previously accumulated interest.

Nominal Rate

The interest rate stated on a financial product or agreement without adjusting for inflation or compounding interest effects.

Compounded Quarterly

The process of calculating interest on the initial amount and any accumulated interest every three months.

Inflation Rate

The pace at which prices for goods and services ascend overall, causing the buying power to decrease.