Math Problem Statement

In Exercises 23-26, find the limit (if possible) of the sequence with the given nth term: - 23. a_n = (n + 1)/n - 24. a_n = 6 + 2/n^2 - 25. a_n = 2n/sqrt(n^2 + 1) - 26. a_n = cos(2/n)

Solution

It looks like you're working on finding the limit of some sequences. The exercise numbers in the image are:

    1. an=n+1na_n = \frac{n + 1}{n}
    1. an=6+2n2a_n = 6 + \frac{2}{n^2}
    1. an=2nn2+1a_n = \frac{2n}{\sqrt{n^2 + 1}}
    1. an=cos⁡(2n)a_n = \cos \left( \frac{2}{n} \right)

Would you like help solving these limits step by step? Let me know if you need detailed solutions for any of these!

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Math Problem Analysis

Mathematical Concepts

Sequences
Limits
Infinite Sequences
Calculus

Formulas

Limit of a Sequence
cosine function
Square Root Function

Theorems

Limit of a Rational Function
Limit of trigonometric functions

Suitable Grade Level

Grades 11-12

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