I have also seen other examples wherein an infinite
series is converged to a finite number.
This is another concept that needs to be discussed in
order to clear up any misunderstanding. When mathematicians write
about a series—any series, including a geometric series, and they
say it is converging absolutely, they are not stating that the
series is completely transforming from an infinite series to a
finite number. They are not saying that now the answer actually is
"2" with no infinite component. Instead they are indicating that a
series of absolute values (all the plus values of a series) are
converging on a finite number. But, it is still understood that the
absolute values are infinite in length and that they will never
reach that finite number.

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