Math Problem Statement

Find the rates of convergence of the following sequences as n → ∞. lim (n → ∞) (2n + 7) / n^2 = 0

Solution

We are tasked with finding the rate of convergence of the sequence:

lim⁡n→∞2n+7n2=0\lim_{n \to \infty} \frac{2n+7}{n^2} = 0

Solution:

We begin by simplifying the given expression:

[ \frac{2n+7}{n^2} = \frac{2n}{n^2} + \frac{7}{n^2} = \frac{2}{n

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Sequences
Limits
Rates of Convergence

Formulas

lim_{n → ∞} f(n) = 0
lim_{n → ∞} (an + b) / cn^2

Theorems

Limit laws for sequences

Suitable Grade Level

College level or Advanced High School

Related Recommendation

Finding the Limit of Sequence S_n = 2n / (n + 3) as n Approaches Infinity

Limit of Sequence a_n = (3n + 1) / (2n^2 + n) as n approaches infinity

Find the Limit of the Sequence u_n as n Approaches Infinity

Determine the Convergence of the Sequence a_n = (n+1/2n)(1 - 1/n)

Convergence Analysis of (2n²)/(n+1) as n → ∞