The limiting sum of the series exists if the absolute value of k is less than 1.
The given series k + k^2 + k^3 + ... is a geometric series where each term after the first is obtained by multiplying the preceding term by k.
The limiting sum exists for a geometric series if the common ratio has an absolute value less than 1.
The common ratio in this case is k, so the limiting sum exists for |k| < 1.
The probable question may be:
For what values of k does the limiting sum exist for the series k + k2 + k3 + ...?