Consider the following statements:I. lim _{n | vedclass

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(A) For statement $I$: $\lim _{n \rightarrow \infty} \frac{2^n+(-2)^n}{2^n} = \lim _{n \rightarrow \infty} (1 + (-1)^n)$.As $n \rightarrow \infty$,the

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$I$ is true and $II$ is false

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(A) For statement $I$: $\lim _{n \rightarrow \infty} \frac{2^n+(-2)^n}{2^n} = \lim _{n \rightarrow \infty} (1 + (-1)^n)$.As $n \rightarrow \infty$,the expression oscillates between $1+1=2$ (for even $n$) and $1-1=0$ (for odd $n$). Therefore,the limit does not exist. Statement $I$ is true.For statement $II$: $\lim _{n \rightarrow \infty} \frac{3^n+(-3)^n}{4^n} = \lim _{n \rightarrow \infty} \left(\frac{3}{4}\right)^n + \left(-\frac{3}{4}\right)^n$.Since $|\frac{3}{4}| < 1$ and $|-\frac{3}{4}| < 1$,both terms approach $0$ as $n \rightarrow \infty$. Thus,the limit is $0+0=0$. Statement $II$ is false.

Consider the following statements:
$I$. $\lim _{n \rightarrow \infty} \frac{2^n+(-2)^n}{2^n}$ does not exist.
$II$. $\lim _{n \rightarrow \infty} \frac{3^n+(-3)^n}{4^n}$ does not exist.
Then,

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Consider the following statements:$I$. $\lim _{n \rightarrow \infty} \frac{2^n+(-2)^n}{2^n}$ does not exist.$II$. $\lim _{n \rightarrow \infty} \frac{3^n+(-3)^n}{4^n}$ does not exist.Then,