Purchase Solution

Real analysis

Not what you're looking for?

Ask Custom Question

Using the definition of convergence of a sequence
show that the following sequences converge to the proposed limit: 1-lim 1/(6n^2+1)=0
2-lim 2/sqrt[n+3]=0
3-lim (3n+1)/(2n+5)=3/2

Purchase this Solution

Solution Summary

This uses the definition of convergence of a sequence to show that sequences converge to the proposed limits.

Solution Preview

Let epsilon> 0 and let N be a natural number such that 1/(6N^2)< epsilon. Then if n>= N we will have:
|1/(6n^2+1)|< |1/(6n^2)|<= |1/(6N^2)|< epsilon
And that is what we were ...

Purchase this Solution

Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts