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.
It looks like this:
X power series
(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 to0.
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