Let ( a n </msub> ) be a bounded sequence of positive real numbers such that <

oleifere45

oleifere45

Answered question

2022-06-22

Let ( a n ) be a bounded sequence of positive real numbers such that lim n a 1 a n n = 1. Prove that lim n a 1 + + a n n = 1.

Answer & Explanation

Xzavier Shelton

Xzavier Shelton

Beginner2022-06-23Added 26 answers

This is false. Consider the sequence
a j = { 2 if  j  is odd 1 2 if  j  is even
we have for all n
1 ( a 1 . . . a n ) 1 n 2 1 n
Thus
lim n ( a 1 . . . a n ) 1 n = 1
But
lim n j = 1 2 n a j 2 n = lim n 2 n + 1 2 n 2 n = 5 4 .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?