What is the sum of these infinite series in statistics?

In summary, the conversation discusses three potential infinite series sums, including ( E(1/n^2) 1 to infinite ), ( E(1/(L+n^2)) 0 to infinite ), and ( E(a^n) 0 to infinite where n is between 0 and 1). The participants are unsure which one is the correct one and are seeking assistance in calculating the sum. The first and third series have simple solutions, but the second does not have a closed form.
  • #1
freedominator
5
0
My statistics professor wanted me to remember an infinite series sum, but i can't remember what it was
i think it was either ( E(1/n^2) 1 to infinite ) or ( E(1/(L+n^2)) 0 to infinite ) or ( E(a^n) 0 to infinite where n is between 0 and 1)
i think it was the 2nd one, does anyone know how to calculate either of these?
 
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  • #2
E should be the sum symbol(##\Sigma##)?
The first one has a simple solution, I don't think I ever saw any closed form for the second.
At the third one, do you mean "a is between 0 and 1"? In that case, it has a nice value as well, which is very useful to know.
 

FAQ: What is the sum of these infinite series in statistics?

What is an infinite series in statistics?

An infinite series in statistics is a sum of an infinite number of terms, where each term represents a specific value or data point. It is used to analyze and understand patterns in data that may continue indefinitely.

How is an infinite series used in statistics?

Infinite series are used in statistics to estimate and calculate the probability of an event occurring, to model data, and to make predictions about future outcomes based on patterns observed in the data.

What are some common types of infinite series in statistics?

Some common types of infinite series used in statistics include geometric series, power series, and Taylor series. Each type has its own characteristics and is useful for different types of data analysis.

What are the challenges of working with infinite series in statistics?

The main challenge of working with infinite series in statistics is that they are, as the name suggests, infinite. This means that they cannot be calculated or analyzed in their entirety, and instead, approximations and estimations must be used. Additionally, the convergence or divergence of an infinite series can be difficult to determine.

How are infinite series related to other mathematical concepts in statistics?

Infinite series are closely related to other mathematical concepts in statistics, such as sequences, limits, and integrals. These concepts are used to understand and analyze the behavior of infinite series and make predictions about the data being studied.

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