Which of the following series could be tested for convergence/divergence with the integral test?

Question

Which of the following series could be tested for convergence/divergence with the integral test?

1. 
2. 
3. 

	I only
	II only
	III only
	All of them

Answer 1

#1 only is the best answer choice, since we can look at the improper integral ∫₁^∞ 1/(1 + x²)dx = arctanx]₁^∞ = π/4. Since the improper integral has a limit, so too does the infinite series (the limits are ≠ , btw). But the two converge or diverge together, which is the premise of the integral test.

Btw, it should be noted that the convergence of #1 implies the convergence of #3 (since the sequence converges absolutely, the alternating series also converges).