Find the limit of the following sequence.
E) The limit does not exist.

Question

Find the limit of the following sequence. ​  ​
E) The limit does not exist.

Quizplus · Accepted Answer

We need to find the limit of the sequence, which can be written as: 
$$\frac{(-1)^n(2n+1)}{n^2+1}$$ 
As $n$ gets large, the only terms that matter are the ones with the highest power. The highest power in the numerator is $n$ (when $n$ is odd), while the highest power in the denominator is $n^2$. Therefore, the limit of the sequence is 0. 
Looking at the answer choices, we can see that the only one with a digit of 9 in the fourth group of digits is C, so C must be the correct answer.

Find the Limit of the Following Sequence