Taylor Series Proof

[fluid sail]

Does anyone know how to proof this Theorem? I think the mean value Theorem could be helpful but I'm lost on where to start. Help!

[neon jolt]

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[rain pulsar]

I think the hardest part here is proving that, if $f(x) = g(x)$ within some neighborhood of 0, then $f^{(n)}(x) = g^{(n)}(x)$ within some neighborhood of 0.

[remote remnant]

Techie Literate

[rain pulsar]

Because following that, it's just a proof by strong induction.

[empty wren]

@fluid sail

:HelpIcon:| Help Reminder

Hello jaychen6328, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.

[halcyon jetty]

why would you have to prove that?

[rain pulsar]

Actually, this is trivial. Sorry for not noticing it.