Math Problem Statement
Solution
The problem asks to investigate the convergence of the series:
using the comparison test ("признак сравнения").
Step 1: Simplifying the General Term
The general term of the series is:
For large , the term in the denominator dominates the constant 1, so we can approximate:
[ a_n \approx \frac{3^n}{4^n} = \left(\frac{3}{4}\right)^n \
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Math Problem Analysis
Mathematical Concepts
Series
Convergence
Comparison Test
Formulas
a_n = 3^n / (4^n + 1)
(3/4)^n for comparison
Theorems
Comparison Test for Series Convergence
Suitable Grade Level
University Level
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