What you can conclude about functions if f(x)*g(x)= (a finite number) and f(x) is tending to infinity and g(x) is tending to zero for a given value of x?

Can I replace f(x) by a diverging series and g(x) by a converging series (which converges to zero).

What is conclusion when I replace n by diverging series and r by a converging series?

It might seems foolishness but what can we conclude if we replace function by numbers such that one number tends to infinity while other tends to zero.

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