# What is the sequence of 1 n?

## What is the sequence of 1 n?

If a sequence is not bounded, it is an unbounded sequence. For example, the sequence 1/n is bounded above because 1/n≤1 for all positive integers n. It is also bounded below because 1/n≥0 for all positive integers n. Therefore, 1/n is a bounded sequence.

Does the sequence n converge?

If we say that a sequence converges, it means that the limit of the sequence exists as n → ∞ n\to\infty n→∞. If the limit of the sequence as n → ∞ n\to\infty n→∞ does not exist, we say that the sequence diverges. If the limit exists then the sequence converges, and the answer we found is the value of the limit.

### Does the sequence 1 n diverge?

n=1 an diverges. n=1 an converges if and only if (Sn) is bounded above.

How do you find the limit of a sequence?

There is no general way of determining the limit of a sequence. Also, not all sequences have limits. However, if a sequence has a limit point, it must be unique. (This is an elementary result of analysis).

#### Does cos(n) converge or diverge?

It is trivial that sin(x) and cox(x) converge as, say, x goes to 0 or, for that matter to any real number. Yes, both sin(x) and cos(x) diverge as x goes to infinity or -infinity. It is not because they “both have upper and lower bound”.

What is the convergence of a sequence?

Procedure for Proving That a Defined Sequence Converges State the Sequence. Our sequence would be defined by some function based on the natural numbers in order for this procedure to work. Find a Candidate for L. Before beginning our proof, we need to find a possible candidate for our limit. Let Epsilon Be Given.

## How do you calculate arithmetic series?

An arithmetic series is the sum of an arithmetic sequence. We find the sum by adding the first, a 1 and last term, a n, divide by 2 in order to get the mean of the two values and then multiply by the number of values, n: