Question
Show that $a_{\mathrm{k}}=\frac{f^{(k)}(0)}{k !}$ where the symbol $$k !=k(k-1)(k-2) \cdots 2 \cdot 1 . \text { Thus, } 4 !=4(3)(2)(1)=24 . \text { The symbol }$$ 0! is defined to be equal to 1 . The symbol " $"$ is read factorial.
Step 1
The Taylor series expansion is given by: \[f(x) = \sum_{k=0}^{\infty} a_k x^k\] where $a_k$ are the coefficients of the series. Show more…
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