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.
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) $\displaystyle \frac{3\pi}{16} \approx 0.58904$