How to Find the Sum of 2^n/n! for n=2 to Infinity

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In summary, the purpose of finding the sum of 2^n / n is to understand its behavior and growth, with applications in fields such as computer science, physics, and economics. The formula for calculating the sum is S = 2^1/1 + 2^2/2 + 2^3/3 + ... + 2^n/n, also known as the geometric series formula. This series is closely related to the exponential function, with the sum approaching the value of 2^n as n approaches infinity. The sum can be calculated using various methods, such as a calculator, computer program, or mathematical techniques.
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kj13529
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I need to find the sum of 2^n/n! from n=2 to infinity, i know that it converges to e^x but how do i find the sum?
 
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kj13529 said:
I need to find the sum of 2^n/n! from n=2 to infinity, i know that it converges to e^x but how do i find the sum?

It is e^2.
Since x^n/n! sums to e^x substitute x=2 to get answer.
 
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Thanks, it was so simple -.-
 

FAQ: How to Find the Sum of 2^n/n! for n=2 to Infinity

What is the purpose of finding the sum of 2^n / n?

The purpose of finding the sum of 2^n / n is to understand the behavior and growth of this mathematical series. This can be useful in various fields such as computer science, physics, and economics.

What is the formula for finding the sum of 2^n / n?

The formula for finding the sum of 2^n / n is S = 2^1/1 + 2^2/2 + 2^3/3 + ... + 2^n/n. This formula is also known as the geometric series formula.

What are the applications of finding the sum of 2^n / n?

There are various applications of finding the sum of 2^n / n. For example, in computer science, this series can be used to analyze the efficiency of algorithms and in economics, it can be used to model population growth.

What is the relationship between the sum of 2^n / n and the exponential function?

The sum of 2^n / n is closely related to the exponential function. In fact, as n approaches infinity, the sum approaches the value of the exponential function 2^n. This is because the terms in the series become increasingly smaller with each iteration.

How can we calculate the sum of 2^n / n in practice?

Calculating the sum of 2^n / n can be done using various methods such as using a calculator, writing a computer program, or using mathematical techniques such as the geometric series formula. The method used will depend on the specific scenario and desired level of accuracy.

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