What Is the General Term of the Series $1-\frac{x^{5}}{5 !}+\frac{x^{10}}{10 !}-\frac{x^{15}}{15 !}+\cdots$

question 41

Multiple Choice

What is the general term of the series $1-\frac{x^{5}}{5 !}+\frac{x^{10}}{10 !}-\frac{x^{15}}{15 !}+\cdots$ ?

• A) \(\frac{(-1)^{k} x^{5 k}}{(5 k) !}\) for \(k \geq 0\)
• B) \(\frac{(-1)^{k+1} x^{5 k}}{(5 k) !}\) for \(k \geq 0\)
• C) \(\frac{(-1)^{k} x^{5 k+5}}{(5 k+5) !}\) for \(k \geq 0\)
• D) \(\frac{(-1)^{k+1} x^{5 k+1}}{(5 k+1) !}\) for \(k \geq 0\)

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