The sum ∑(from n = 1 to ∞) arctan [n/(n^4 - 2n^2 + 2)] is equal to:

A) (arctan 2 + arctan 3)/4

B) 4. (arctan 1)

C) -π/16

D) 3π/16

More than one options may be correct.

Printable View

- Aug 13th 2008, 06:57 AMfardeen_genThe sum of the trigonometric series...?
The sum ∑(from n = 1 to ∞) arctan [n/(n^4 - 2n^2 + 2)] is equal to:

A) (arctan 2 + arctan 3)/4

B) 4. (arctan 1)

C) -π/16

D) 3π/16

More than one options may be correct. - Aug 14th 2008, 09:13 AMfardeen_gen
To be more precise, it is http://alt1.artofproblemsolving.com/...7ebfe69b99.gif = ?

- Aug 14th 2008, 10:09 AMwingless
None of them is correct.

$\displaystyle \sum_{n=1}^\infty \arctan \frac{n}{n^4-2n^2+2} \approx 1.072215$

A) $\displaystyle \frac{\arctan 2 + \arctan 3}{4} \approx 0.58904$

B) $\displaystyle 4 \arctan 1 = 4 \frac{\pi}{4} = \pi \approx 3.14159$

C) $\displaystyle -\frac{\pi}{16} \text{ is negative \dots}$

D) $\displaystyle \frac{3\pi}{16} \approx 0.58904$ - Aug 15th 2008, 05:19 AMfardeen_gen
One of the answers is definitely true - this was what my instructor told me. Are you sure wingless that the the given sum is not equal to any of the options??