The limit of the expression as x approaches 1 is derived using the formula for the sum of a geometric series. The limit can be rewritten to eliminate indeterminate forms by factoring out (x-1) from both the numerator and denominator. This leads to the simplified limit expression, which evaluates to the ratio of the sums of constants, resulting in m/n. The calculations confirm that as x approaches 1, the limit converges to m/n, where m and n are natural numbers. This demonstrates the relationship between the powers of x in the limit.