Convergence of Sequences

We say a sequence of real numbers

converges to if for every

there is a number

such that for every

, we have

. This means that no matter how small

is, after some point (the

term), every term will be within

. Below you can input a sequence

and choose a value of

. Then you can see the terms in your sequence that are within

of the limit. If you can continue to make

smaller and smaller, and there is always a point at which the sequence is within that distance of

, then your sequence converges.

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