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bcucinel
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Homework Statement
It can be shown that ∑(n=1) to (n=∞) of 1/n² = π²/6
use this fact to show that ∑(n=1) to (n=∞) of 1/(2n-1)² = π²/8
What have you tried? You need to make an attempt at a solution before anyone can give you any help.bcucinel said:Homework Statement
It can be shown that ∑(n=1) to (n=∞) of 1/n² = π²/6
use this fact to show that ∑(n=1) to (n=∞) of 1/(2n-1)² = π²/8
Homework Equations
The Attempt at a Solution
Now, can you manipulate this series--Σ1/(2n)²--to get to something you know?bcucinel said:1/4+1/16+1/36+...
Σ1/n² - Σ1/(2n-1)² then equals Σ1/(2n)² from n=1 to infinity
bcucinel said:Thank you, I understand all of that perfectly... The issue I am having with the problem, however, is that I don't recall ever being taught in my calculus class exactly how to determine the Sn of a series like Σ1/(2n)²... If there is some technique that I could use please let me know.
To calculate a summation, you need to add up a series of numbers. The formula for calculating a summation is ∑x = x1 + x2 + x3 + ... + xn, where x represents the numbers in the series and n represents the total number of terms.
Calculating a summation is used to find the total of a series of numbers. It is commonly used in mathematics and science to analyze data and make predictions based on patterns in the data.
The most common notation used for summations is the sigma notation, which is represented by the Greek letter ∑. Other notations include the capital letter S and the word "sum" written above the series of numbers.
There are a few strategies that can be used to simplify a summation, including factoring out common terms, using algebraic properties, and breaking the summation into smaller parts. It is also helpful to have a thorough understanding of basic arithmetic and algebra.
A summation is closely related to integrals and derivatives, as all three concepts involve finding the total or change of a function. In fact, integrals and derivatives can be used to evaluate certain types of summations, particularly those involving continuous functions.