Given That the Power Series For $\frac { 1 } { 1 - x }$

question 296

Essay

Given that the power series for $\frac { 1 } { 1 - x }$ is $\sum _ { n = 0 } ^ { \infty } x ^ { n }$ , find the power series for $\frac { 1 } { ( 1 - x ) ^ { 2 } }$ in terms of powers of x.

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Definitions:

Independent Variable

A variable in statistical modeling that is manipulated or categorized to observe its effect on a dependent variable.

Stepwise Regression

An approach to constructing regression models where the selection of predictor variables is performed automatically.

Dependent Variable

A variable in an experiment or model that is expected to change in response to manipulations of independent variables.

Building Model

The process of creating a mathematical, statistical, or computational representation of a real-world scenario for the purpose of analysis or prediction.