What is the power series of f(x)= ln(5-x)? What is it’s radius of convergence?

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Since the ##int1/(5-x)##= ##ln(5-x)## get the strength sequence fidelity of ##1/(5-x)##. Algebraically touch the equation to get the equation for the sum of the (which is ##Sn= a/(1-r)## ).

Using this we could use the strength sequence fidelity of the geometric sequence ##sumar^(n)## such that ##a=1/5## and ##r=x/5## Substituting this in the pwer sequence equation, we get

##sum(1/5)(x/5)^n##.

Integrate this strength sequence fidelity to get thestrength sequence of ##ln(5-x)##. ##int####sum(1/5)(x/5)^n##. = ##sum(1/(5(n+1)))(x/5)^(n+1)##.

Use Ratio Test on ##sum(1/(5(n+1)))(x/5)^(n+1)## to get the Radius and Interval of Convergence.

For IOC, do not foget to designate mob/divergence at end points to designate if interposed in the ##domf## or not

In getting Radius of Convergence, it must be in this mould, ##abs(x-c)####< 1## such that the sequence is centered at c.

R=5 (radius of mob)

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