Exercise 3.10

Question

Exercise 10:
    Suppose that the coefficients of the power series $\sum a_nz^n$ are integers, infinitely many of which are distinct from zero. Prove that the radius of convergence
    is at most 1.

ghostofgarborg · Accepted Answer

If $|z| \geq 1$ and $a_n 
eq 0$ for an infinite number of values of $n$, then $|a_n z^n| \geq |a_n|$, 
    and does not tend to $0$. This makes the series divergent when $|z| \geq 1$.

Exercise 3.10

Answers

Comments

Exercise 3.10

Answers

Comments

Add answer