Question
Find the linit of the following sequence or determine that the sequience diverges \( \left\{\frac{2^{n+1}+3}{2^{n}}\right\} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The limit of the sequence is B. The (Type an exact answer.) Bequence diverges.
Ask by Bowman Chang. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The limit of the sequence is 2.
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The Deep Dive
To find the limit of the sequence \( \left\{ \frac{2^{n+1} + 3}{2^n} \right\} \), we can simplify the term: \[ \frac{2^{n+1} + 3}{2^n} = \frac{2 \cdot 2^n + 3}{2^n} = 2 + \frac{3}{2^n}. \] As \( n \) approaches infinity, the term \( \frac{3}{2^n} \) approaches zero. Therefore, the limit of the sequence is: \[ 2 + 0 = 2. \] So, the correct choice is: A. The limit of the sequence is 2.