How do I find the greatest lower bound for the sequence A={1n+10}^∞_n=1?

foyerir

foyerir

Answered question

2022-09-08

How do I find the greatest lower bound for the sequence A = { 1 n + 10 } n = 1 ?

Answer & Explanation

wegpluktee3

wegpluktee3

Beginner2022-09-09Added 12 answers

We seek upper and lower bounds for the sequence:
{ 1 n + 10 } for n [ 1 , )
If we consider the function:
f ( x ) = x + 10
Then trivially, f(x) is monotone increasing and so 1 f ( x ) is monotone decreasing.
Thus we have an upper bound when n=1 corresponding to:
supremum = 1 f ( 1 ) = 1 11
And a lower bound as n corresponding to:
infimum = lim n 1 f ( n ) = lim n 1 n + 10 = 0

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?