Differentiation Question 28
Question: $ \underset{n\to \infty }{\mathop{\lim }}\sum\limits _{x=1}^{20}{{{\cos }^{2n}}(x-10)} $ is equal to
Options:
A) 0
B) 1
C) 19
D) 20
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ \underset{n\to \infty }{\mathop{\lim }}{{\cos }^{2n}}x= \begin{cases} 1,x=r\pi ,r\in I \\ 0,x\ne r\pi ,r\in I \\ \end{cases} . $
Here, for $ x=10 $ and $ \underset{n\to \infty }{\mathop{\lim }}{{\cos }^{2n}}(x-10)=1 $
And in all other cases, it is zero. Therefore, $ \underset{n\to \infty }{\mathop{\lim }}\sum\limits _{x=1}^{\infty }{{{\cos }^{2n}}(x-10)=1} $
BETA
