The pole of a function is a point where the function becomes undefined, meaning that the function approaches infinity or negative infinity.
The pole of a function can be identified by finding the values of x that make the denominator of the function equal to zero. These values are known as the poles of the function.
A geometric series is a sequence of numbers where each term is found by multiplying the previous term by a constant number, known as the common ratio. It has the form a, ar, ar^2, ar^3, ..., where a is the first term and r is the common ratio.
The pole of a function can be represented as the limit of a geometric series as the number of terms approaches infinity. This means that as x approaches the pole, the function becomes an infinite geometric series.
The pole of a function is important because it can help us understand the behavior of the function near that point. It can also help us identify any discontinuities or asymptotes in the function.