Determine if the functions converge or diverge? I dont know how to do these! Please help by explaining so I can understand! Thanks! Example: (5n^4)+1/((150,348n^3)+999) and how you could do something like this: 2,1, 2/3, 1/2, 2/5   Thanks!

Expert Answers

An illustration of the letter 'A' in a speech bubbles

In math we describe a function Converge or Diverge based on its ending behavior as x approches positive or negative infinity.

If a fuctions approches inf. as x approches positive or negative infinity, then the function is diverge.

On the other hand, If a function approaches a certain value as x apporaches positive or negative inf, then the function is Converge.

In your example :

(5n^4)+1/((150,348n^3)+999)

as n approaches inf., the function approches 0 , so the function is converge to 0.

and the series:

2,1, 2/3, 1/2, 2/5,....

the series is clearly approching 0 as n values approaches inf. then the series is Converge to 0.

 

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial