Calculating cos(2nπ/3)/(n²) using the Sum of Series 1/n²

[andrey21]

Rite so what your saying is:

Pi^2/6 = Pi^2/54 + SUM 1/(3n+1)^2 + SUM 1/(3n+2)^2

 

[micromass]

Yes, so you've found the values to all the series!

 

[andrey21]

Ah ok so:

Pi^2/54 - 1/2(Pi^2/6 - Pi^2/54) = Sum of series

 

[micromass]

Yes! Very good!

 

[andrey21]

Thanks Micromas you have been great help. Out if curiosity how did you obtain the equation in post 35 ??

 

[micromass]

Well, in post 14, we were asked to calculate those two sums. I first tried to evaluate them separately, but that didn't work. So then I came up with that solution. I guess it's a bit experience from my part. The more problems you solve, the more tricks you know. You also know the trick now

 

[andrey21]

Haha ok thanks again micromass

 

[andrey21]

I just finished my calculations and ended up with value of -3Pi^2/54 for sum of series. Is this correct?? Thanks in advance

 

[micromass]

Yes, I believe that is correct!