## P-Series

It is a series as follows:

CONVERTS if p> 1

DIVERGE if p1

If p = 1, the series

it's called **harmonic series** and according to the theorem it is **divergent.**

## Alternating series

It looks like this:

## Power Series

### X power series

or

### (X-c) Power Series

For convenience, let's assume that even when x = 0.

When replacing **x** by a real number, we get a series of constant terms that can converge or diverge.

In any power series of x,** the series always converges to x = 0, **because if we replace** x** per **0** the series comes down to_{0}.

In the power series of (x-c), the **series converges to x = c**.

To determine the other values of **x** for which the series converges, the **test of reason.** Next: Leibniz Test