Complex Analysis/Radius of Convergence question.

[Kemba Huskie]

Homework Statement

Question asks to show that if f is an entire function and bounded then it is polynomial of degree m or less.

Homework Equations

The Attempt at a Solution

I tried plugging in the power series for f(z) and tried/know it is related to Liouville's Theorem somehow but I am just not gaining any traction. A picture of the question is attached below:

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[FactChecker]

Make r big.
Your statement of the problem is wrong if you really mean the inequality of question 21 (in your attempt at a solution). A bounded entire function is a constant.