Apply the Integral Test to ∑n=1∞1n2+1\sum_{n=1}^{\infty} \frac{1}{n^2 + 1}∑n=1∞n2+11. What is ∫1∞dxx2+1\int_1^\infty \frac{dx}{x^2+1}∫1∞x2+1dx?
The integral equals π4\frac{\pi}{4}4π; the series converges
The integral diverges to ∞\infty∞; the series diverges
The integral equals 000; the series converges to 000
The integral equals ln(2)\ln(2)ln(2); the series diverges