Consider the function $f(x)=1-\cos x$ .Is the Maclaurin series for $f(x)$ given by $\sum_{i=1}^{\infty} \frac{(-1)^{i+1} x^{2 i}}{(2 i) !}$ ?

Question

Quizplus · Accepted Answer

The Maclaurin series for $1 - \cos x$ is indeed given by $\sum_{i=1}^{\infty} \frac{(-1)^{i+1} x^{2 i}}{(2 i) !}$, as the series for $\cos x$ is $\sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!}$, and subtracting this from 1 gives the series in question, starting from $i=1$.

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