Math Problem Statement
Using any of the results in this section, prove the following. (d) lim (√ n /(n+1))=0 (e) lim n^2 / n! =0 (f) If Ixl < 1, then lim (n approach infinity)x^n = 0
Solution
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Math Problem Analysis
Mathematical Concepts
Limits
Asymptotic Behavior
Factorial Growth
Sequences and Series
Formulas
lim_{n \to \infty} \frac{\sqrt{n}}{n+1} = 0
lim_{n \to \infty} \frac{n^2}{n!} = 0
lim_{n \to \infty} x^n = 0 (when |x| < 1)
Theorems
Limit of a Function
Factorial Growth Rate
Geometric Series
Behavior of Powers of Numbers Less Than 1
Suitable Grade Level
College Level
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