Find a power series representation for the function and determine the interval of convergence ln(5 - x

To find the power series representation of In(5 - x), we recall that the power series representation of a function of the form:

provided |r| < 1
Also recall that

Notice that

To get the power series of

Therefore, the power series representation of

When x = 0: C = ln 5
Therefore,


The radius of convergence is given by |r| < 1.
Here,

Therefore, radius of convergence is