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Question

Answer 1

20).

The limit of a sequence is the value that the terms of a sequence " tend to ".

If such a limit exists, the sequence is called convergent.

A sequence which does not converge is said to be divergent.

The limit of a sequence is said to be the fundamental notion on which the whole of analysis ultimately rests.

Limits can be defined in any metric or topological space, but are usually first encountered in the real numbers.

Limit of a sequence can be used in the real world :

The notion of limit of a sequence is very natural.

Indeed, consider a scientist who is collecting data everyday.

Set to be the sequence generated by our scientist ( is the data collected after days).

Imagine that after a certain day the numbers are very close to each other.

Therefore, the scientist will decide that the experiment settled down to a equilibrium state, meaning that no change occured to the data.

The danger here is that, though the data collected after that date are closer to each other, in general, expect that the system settles down.