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Question 24 1 pts A sequence {a

n

​

} converges if: BCF31 lim

n→[infinity]

​

a

n

​

does not exist. lim

n→[infinity]

​

a

n

​




=0 None of these lim

n→[infinity]

​

a

n

​

exists.

Answer :

A sequence converges if and only if its limit exists. The limit of a sequence is the value that the terms of the sequence get closer and closer to as n approaches infinity.


A sequence is said to converge if it has a limit, which means that the terms of the sequence get closer and closer to a specific value as n approaches infinity. If the limit does not exist, then the sequence is said to diverge.

In the case of the sequence {an}, the limit is limn→∞an. If this limit exists, then the sequence converges. If the limit does not exist, then the sequence diverges.

The answer is therefore (C), limn→∞an exists.

There are two ways to show that a sequence converges:

* Direct proof: This involves showing that the terms of the sequence get closer and closer to a specific value as n approaches infinity.
* Limit comparison test: This involves comparing the sequence to another sequence that is known to converge or diverge.

The limit comparison test is a powerful tool that can be used to prove the convergence of many different sequences.

Learn more about Sequence click here

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