Answer to Question #246927 in Calculus for Anku

Question

 “The series expansion of the function cosx in powers of x contains all even 

 powers of x only.” True/ False ?

Answer 1

$$\cos x=1-\dfrac{x^2}{2!}+\dfrac{x^4}{4!}-\dfrac{x^6}{6!}+...=\displaystyle\sum_{n=0}^{\infin}(-1)^n\dfrac{x^{2n}}{(2n)!},$$

for all $x.$

“The series expansion of the function cosx in powers of x contains all even 

 powers of x only.”  True.