Alternating Series Error Bound Formula Derivation
By Emily Wilson •
I'm learning about error approximations in my AP Calc. BC class, was given this formula (from Shaw and Taylor Calculus Extended) to define the alternating series error bound:
$$ASR ≤ |\frac{f^{n+1}(c)(x-c)^{n+1}}{(n+1)!}|$$
which is like the Lagrange remainder bound where z=c.
The alternating series error bound is also defined as the next unused term, which means that $a_{n+1} = |\frac{f^{n+1}(c)(x-c)^{n+1}}{(n+1)!}|$.
I haven't been able to resolve any intuition or find any answers as to why these two are equal. Am I missing something?
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