What is the solution to this tricky series riddle?

In summary, the conversation revolves around calculating the sum of 1/(2n + 1)^2 from n=0 to infinity. It is mentioned that the answer is (pi)^2/8, and the person is having trouble solving it. The conversation also mentions using the fact that 1/n^2 = (pi)^2/6 to help solve the problem. Eventually, it is discovered that the sum is equal to (pi)^2/8. The conversation ends with the person apologizing for taking up the expert's time and thanking them for their help.
  • #1
joris_pixie
25
0
Hey, guys !
I have to calculate:

[tex]\sum 1/(2n + 1)^2 [/tex]
n from 0 to infinite

Knowing that 1/n² = (pi)²/6

The answer is (pi)²/8

I don't know why I'm stuck here but I just don't get it...

Greetings
 
Last edited:
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  • #2
Once you have what

[tex]\sum_{n=1}^{ \infty } \frac{1}{n^2}[/tex] is, you should be able to find what

[tex]\sum_{n=1}^{ \infty } \frac{1}{(2n)^2}[/tex] is pretty easily. And then use both of these to find the series sum that you're looking for
 
  • #3
It is given ...
Calculate:
[tex]\sum^{\infty}_{0} 1/(2n +1)^2 [/tex]

if you know that:

[tex]\sum^{\infty}_{1} 1/n^2 = (pi)^2 /6 [/tex]But I can't make it work :(
 
  • #4
Can you calculate this? [tex]
\sum_{n=1}^{ \infty } \frac{1}{(2n)^2}
[/tex]

Then what is [tex]
\sum_{n=1}^{ \infty } \frac{1}{(2n)^2} + \sum_{n=0}^{ \infty } \frac{1}{(2n+1)^2}
[/tex]
 
  • #5
haha I'm sorry for wasting your time !
It was infact not hard, but had a few drinks too much last night.

http://www.pixie.be/solution.JPG thank you anyway !
 
Last edited by a moderator:

1. What is a series in terms of riddles?

A series in riddles refers to a sequence of clues or questions that are presented to the solver in a specific order. The solver must use logic and critical thinking to decipher the series and arrive at the correct answer.

2. How do I solve a series riddle?

To solve a series riddle, you must carefully read and analyze each clue or question in the series. Look for patterns, similarities, and connections between the clues to help you arrive at the correct answer. It may also be helpful to write down the clues in a list or diagram to visually organize the information.

3. Are there different types of series riddles?

Yes, there are various types of series riddles, such as numerical series, alphabetical series, and logical series. Each type requires a different approach to solving, but they all follow the same principle of using clues to arrive at the answer.

4. Is there a specific strategy for solving series riddles?

There is no one-size-fits-all strategy for solving series riddles, as each riddle is unique and may require a different approach. However, some tips for solving series riddles include paying attention to details, thinking outside the box, and using deductive reasoning.

5. Can I create my own series riddles?

Yes, anyone can create their own series riddles. It takes creativity, critical thinking, and a good understanding of how series riddles work. You can start by practicing with existing riddles and then try making your own with a unique twist or theme.

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