Find an Expression for the General Term of the Taylor $x \sin x=x^{2}-\frac{x^{4}}{3 !}+\frac{x^{6}}{5 !}-\frac{x^{8}}{7 !}$

question 5

Multiple Choice

Find an expression for the general term of the Taylor series for $x \sin x=x^{2}-\frac{x^{4}}{3 !}+\frac{x^{6}}{5 !}-\frac{x^{8}}{7 !}$ .

• A) \(\frac{(-1)^{n-1} x^{2 n-1}}{(2 n+1) !}\)
• B) \((-1)^{2 n-1} \frac{x^{n+1}}{n !}\)
• C) \((-1)^{n} \frac{x^{2 n+2}}{(2 n+1) !}\)
• D) \(\frac{x^{2 n}}{2 n-1}\)

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