3) 

Remember the statement of the integral test: if f(x) is positive and decreasing, and  a[n] = f(n), then   converges if and only if    converges (i.e. if the integral converges, so does the sum and if the integral diverges, so does the sum.)  Consider the series   .  First check that the terms of this series do in fact decrease by taking a derivative; what is the interval on which it decreases?  Then use the integral test to determine if it converges or diverges. But note that this test does NOT give you the actual sum of the series; it only tells you if it converges or diverges.  To see this, sum the series.  Use the "evalf" command to doublecheck that the sum of the series is not equal to the value of the integral.