Determine the convergence or divergence of the series. sum_{n=1}^inftyfrac{n}{sqrt{3n^2+3}}

Alyce Wilkinson 2020-11-08 Answered
Determine the convergence or divergence of the series.
n=1n3n2+3
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

averes8
Answered 2020-11-09 Author has 92 answers
Consider the given series n=1n3n2+3
Divergence test series,
If limnan0 then series n=1an is diverge
And
If limnan=0 then series n=1an is is convergence or diverge
Given an=n3n2+3
Now find the limit
limnan=limnn3n2+3
=limnnn3+3n2
=limnnn3+3()2
=13
Hence, the series is divergence because limnan0
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-12-25
I am having difficulty finding if this series converges or diverges:
n=0(2)n+1nn1
I am unsure of which test to use. At first, I thought I should use alternating series test, but I am unable to manipulate the numerator to (1)n+1. I thought I may be able to use root test, but I have no clue how to manipulate the series to do that.
What series test would I use, and how?
asked 2022-02-23
Prove
3π8=k0(15)kF2k+12k+1q2k+1
where q=2+221+17+825, and Fn are the Fibonacci numbers.
asked 2020-11-24
Use the limit Comparison Test to detemine the convergence or divergence of the series.
n=15n+n2+4
asked 2021-01-15
It is important to distinguish between
n=1nb and n=1bn
What name is given to the first series? To the second? For what values of b does the first series converge? For what values of b does the second series converge?
asked 2020-11-23
Determine if the series n=0an is convergent or divergent if the partial sum of the n terms of the series is given below. If the series is convergent, determine the value of the series.
Sn=5+8n227n2
asked 2022-01-23
How to calculate 01xxdx using series? I read from a book that
01xxdx=1122+133++(1)n1(n+1)n+1+
asked 2022-02-18
Use the Root Test to determine the convergence or divergence of the series. n=1(n3n+1)n