8.3. Series and Power Series

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).

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