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## Homework Statement

I had this question on a test. No one I talked to had a clue how to solve it, and our professor will not be publishing solutions. Any insight as to how to aproach this would be great because I am totally stumped.

Let [tex] f \in C^\infty[-1,1] [/tex] such that for all [tex] j \in N |f^{(j)}|<M [/tex]. given that [tex] f(1/k)=0 \forall k \in N [/tex] prove that [tex] f=0 [/tex] in [tex] [-1,1] [/tex]

## The Attempt at a Solution

The only idea I've had is that I need to use the taylor series. But I have no idea what to do with it.

Thanks

Tal