Half-range sine series.

Check my work,
Either I have done some mistake or its a tricky deduction!

How would i deduce that ?

Question

Half-range sine series.

Check my work,
Either I have done some mistake or its a tricky deduction!

How would i deduce that ?

anonymous · Answer

I can't see the problem...

hartnn · Answer

attachment

hartnn · Answer

the problem is i have a "n^3" in the denominator
whereas the deduction requires
1/3^2 , 1/5^2 ....so 1/n^2

hartnn · Answer

@phi 
@ganeshie8

phi · Answer

my version of word can't read your file.

hartnn · Answer

attachment

hartnn · Answer

attachment

hartnn · Answer

OMG, did they just do a typing error and in the question there actually should be cubes and not squares ??

still i get this, 1/12 missing...

hartnn · Answer

$π^3/32=1/1^3 -1/3^3 +1/5^3 -1/7^3 +..… $

hartnn · Answer

i think they meant 1/1^2 
which is still incorrect

hartnn · Answer

and 
$π^3/32=1/1^3 -1/3^3 +1/5^3 -1/7^3 +..…$

is what they want

phi · Answer

Yes, your work is good, and their summation is something entirely different as you probably figured out.

phi · Answer

$$ \frac{\pi^3}{32} = \sum_{k=0}^\infty \frac{(-1)^k}{(2k+1)^3} $$

hartnn · Answer

thanks for the confirmation! :)