A) 0
B) 1
C) 19
D) 20
Correct Answer: B
Solution :
[b] \[\underset{n\to \infty }{\mathop{\lim }}\,{{\cos }^{2n}}x=\left\{ \begin{matrix} 1,x=r\pi ,r\in I \\ 0,x\ne r\pi ,r\in I \\ \end{matrix} \right.\] 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, \[\underset{n\to \infty }{\mathop{\lim }}\,\sum\limits_{x=1}^{\infty }{{{\cos }^{2n}}(x-10)=1}\]
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