Example 8.3.4 (b): Function Series Examples
On which interval does the series f(x) = 32nxn represent a continuous function?
Let's compute the sup-norm:
|| 32nxn ||[-r, r] = (9r)n
The numeric series (9r)n is finite iff 9r < 1 or equivalently r < 1/9.
Thus, our series converges absolutely and uniformly to a continuous function on every closed subset of (-1/9, 1/9).