Question

How does Galitskii's integral converge?

Answer 1

the limit does not exist or it is infinite, then we say that the improper integral is divergent. If the improper integral is split into a sum of improper integrals (because f(x) presents more than one improper behavior on [a,b]), then the integral converges if and only if any single improper integral is convergent.
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Answer 2

Explanation:

∑ n = 1 ∞ 1 n 2 = 1 1 2 + 1 2 2 + 1 3 2 + 1 4 2 + ⋯ The Integral Test compares an infinite series to an improper integral in order to determine convergence or divergence.