A student wishes to analyze the convergence of the series n=1∑∞(−1)n−1n+1n by evaluating an improper integral. Which of the following approaches is valid?
a) Integrate (−1)x−1x+1x from 1 to ∞ using the Integral Test.
b) Integrate x+1x from 1 to ∞ and compare the result with the series of absolute values.
c) Integrate x+1x from 1 to ∞; since the integral diverges, conclude that the alternating series diverges as well.
d) Replace x+1x by x1 and apply the p–integral test, asserting convergence because p=21>1.