Question

an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number or ∞ or −∞ or, in some cases, as both endpoints approach limits. Such an integral is often written symbolically just like a standard definite integral, perhaps with infinity as a limit of integration. But that conceals the limiting process.

Answer 1

can you please at least attach a file of it?

Answer 2

You forgot to put it as an equation...\[\large \lim_{b\to\infty}\int\limits\limits_1^b \frac{1}{x}\,\mathrm{d}x = \infty\]

Answer 3

Is it possible in convergence does not make sense as a question.
You're asking whether a particular integral converges?

Answer 4

give first a concrete example