How to show the following summation is true?

Thread starter Bishop556
Start date Mar 31, 2015
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Summation

In summary, A summation is a mathematical operation that involves adding a sequence of numbers together. To show that a summation is true, you can use various mathematical techniques such as induction, direct proof, or contradiction. The notation for a summation is ∑ (the Greek letter sigma) followed by the expression being summed, the index of summation, and the limits of the summation. Yes, a summation can be rewritten in various forms, such as using sigma notation, factorial notation, or telescoping sums. You can use mathematical properties such as the distributive property, associative property, and commutative property to manipulate a summation and show that it is true.

Mar 31, 2015

Bishop556

I need to prove that the following summation is true:

∑(-1)^n * cos(nx) / n^2 = (3x^2 - π^2)/12

How would I tackle this problem?

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Apr 1, 2015

Svein

Science Advisor

Insights Author

Hint: [itex]\sum_{n=1}^{\infty}\frac{1}{n^{2}}=\frac{\pi^{2}}{6} [/itex]

1. What is a summation?

A summation is a mathematical operation that involves adding a sequence of numbers together.

2. How do you show that a summation is true?

To show that a summation is true, you can use various mathematical techniques such as induction, direct proof, or contradiction.

3. What is the notation for a summation?

The notation for a summation is ∑ (the Greek letter sigma) followed by the expression being summed, the index of summation, and the limits of the summation.

4. Can a summation be rewritten in another form?

Yes, a summation can be rewritten in various forms, such as using sigma notation, factorial notation, or telescoping sums.

5. How can you use mathematical properties to prove a summation is true?

You can use mathematical properties such as the distributive property, associative property, and commutative property to manipulate a summation and show that it is true.