Find the Sum of the Infinite Geometric Series $\frac { 2 } { \sqrt { 2 } } + 1 + \frac { 1 } { - \sqrt { 2 } } + \frac { 1 } { 2 } + \cdots$

question 63

Essay

Find the sum of the infinite geometric series $\frac { 2 } { \sqrt { 2 } } + 1 + \frac { 1 } { - \sqrt { 2 } } + \frac { 1 } { 2 } + \cdots$ .

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Definitions:

Exponential Smoothing

A time series forecasting method for univariate data that applies decreasing weights to past observations, with the most weight given to the latest data.

Indicator Variables

Variables used in statistical models that take the value 1 if a certain condition is met and 0 otherwise, often used for representing categorical data.

Seasonal Variations

Periodic fluctuations in time series data that occur at regular intervals due to seasonal factors.

Stock Market Performance

An indicator of the overall health and activity of the stock market, often reflected through indexes like the Dow Jones or S&P 500.