Question

What is the comparison test exactly? And how would you use the comparison test to do this problem?

Answer 1

C

Explanation:

If you have two functions such that 0 < g(x) < f(x) for all values of x on a domain, then g(x) converges if f(x) converges, and f(x) diverges if g(x) diverges.

Basically, if a known function converges, then a smaller function also converges. And if a known function diverges, then a larger function also diverges.

1/√x is a p-series where p = ½, so this integral diverges.

1/(√x − 1) is larger than 1/√x on the domain 2 ≤ x ≤ ∞. So if 1/√x diverges, then 1/(√x − 1) also diverges.