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V150
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Homework Statement
Suppose that [itex]f(x)=\sum_{n=0}^{\infty}c_{n}x^{n}[/itex]for all x.
If [itex]\sum_{n=0}^{\infty}c_{n}x^{n} = 0[/itex], show that [itex]c_{n} = 0[/itex] for all n.
Homework Equations
The Attempt at a Solution
I know, by using taylor expansion, [itex]c_{n}=\frac{f^{n}(0)}{n!}[/itex], and because [itex]\sum_{n=0}^{\infty}c_{n}x^{n}[/itex] is zero, [itex]c_{n}[/itex] have to be zero. But, I don't know how to write more logical proof to this.