Question

$\underset{n\to \infty }{lim}\sum _{n=1}^{20}{\cos }^{2n}(x-10)$ is equal to

• A. 0
• B. 1
• C. 19
• D. 20

Answer 1

Answer: (B)

1

$\underset{n\to \infty }{lim}{\cos }^{2n}x=\{\begin{array}{ccc}1,& x=r\pi ,& r\in I\\ 0,& x\ne r\pi ,& r\in I\end{array}\text{Here, for x = 10,}\underset{n\to \infty }{lim}{\cos }^{2n}(x-10)=1\text{and in all other cases, it is zero. Therefore,}\underset{n\to \infty }{lim}\sum _{n=1}^{\infty }{\cos }^{2n}(x-10)=1$