Question
Use a Taylor series to verify the given formula.$$\sum_{k=0}^{\infty} \frac{(-1)^{k} \pi^{2 k+1}}{(2 k+1) !}=0$$
Step 1
Step 1: First, let's recall the Taylor series for the sine function, which is given by: $$ \sin(x) = \sum_{k=0}^{\infty} \frac{(-1)^{k} x^{2 k+1}}{(2 k+1) !} $$ This series converges for all $x$ and equals to $\sin(x)$ for all $x$. Show more…
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