Finding the Limit of a Complex Sequence

Click For Summary
The limit of the sequence a(n)=[n+(-1)^n. sqrt(n)]/[(n^2 +1)^1/2] is being analyzed as n approaches infinity. The discussion suggests that the sequence oscillates and tends towards 1. Participants consider using L'Hôpital's rule and dividing the numerator and denominator by n to simplify the expression. The behavior of each term in the sequence is crucial for determining the limit. Ultimately, the consensus is that the limit exists and is equal to 1.
Fairy111
Messages
72
Reaction score
0

Homework Statement



What is the limit of the following sequence, if it exists?

Homework Equations



a(n)=[n+(-1)^n. sqrt(n)]/[(n^2 +1)^1/2]

The Attempt at a Solution



Can i use l'hopitals rule? Or if not, how should i do this particular question?
 
Physics news on Phys.org
I'd imagine as n \rightarrow \infty?

In that case, looks like it's going to oscillate back and forth dwindling down to 1.
 
Yea...as n tends to infinity. What were your steps to working out that it tends towards 1?
 
Divide the numerator and the denominator by n. Think about the behavior of each term.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

A question about definite integrals and series limits
  • · Replies 12 ·
Replies
12
Views
2K
How to show that these sequences are summable?
  • · Replies 1 ·
Replies
1
Views
2K
Help calculating this limit please
  • · Replies 5 ·
Replies
5
Views
1K
Finding limit of the Fibonacci sequence
  • · Replies 8 ·
Replies
8
Views
2K
Unit normed linear functional on a space of sequences
  • · Replies 13 ·
Replies
13
Views
2K
Converging Vs diverging sequences
  • · Replies 4 ·
Replies
4
Views
2K
Prove that this series converges uniformly on R
  • · Replies 4 ·
Replies
4
Views
2K
Bounded and monotonic sequences - Convergence
  • · Replies 7 ·
Replies
7
Views
2K
Doubt regarding the series ##\sum [\sqrt{n+1} - \sqrt{n}\,]##
  • · Replies 17 ·
Replies
17
Views
2K
Understanding the Use of Min in Cauchy Sequences
  • · Replies 1 ·
Replies
1
Views
1K