Which of the following sequences are convergent sequences? 1) a n </msub> =

Dennis Montoya

Dennis Montoya

Answered question

2022-05-12

Which of the following sequences are convergent sequences?
1) a n = 7 n n 7
2) a n = 1 n
3) a n = 1 7 + ( 1 ) n
4) a n = cos ( n ) n
5) a n = 7
6) a n = 7

Answer & Explanation

lutzantsca885

lutzantsca885

Beginner2022-05-13Added 15 answers

1) a n = 7 n n 7
We know that
n 7 < 7 n
7 n n 7 > 1
lim n a n = lim n 7 n n 7
=
Thus, the sequence is not convergent

2) a n = 1 n
lim n a n = lim n 1 n = 0
Thus, the sequence is convergent

3) a n = 1 7 + ( 1 ) n
For n – odd
a n = 1 7 1 = 6 7
For n – even
a n = 1 7 + 1 = 8 7
The sequence is not convergent as the limit of subsequence convergent to different limits

4) a n = cos ( n ) n
lim n a n = lim n cos ( n ) n = 0 (cos(n) is bounded)
Thus, the sequence is convergent
Reese Estes

Reese Estes

Beginner2022-05-14Added 4 answers

5.
a n = 7 is constant sequence
lim n
It is convergent

6.
a n = 1 7 is constant sequence
lim n a n = 1 7
It is convergent

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?