The sequence is .

The first ten terms of the sequence are

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.

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.

.

.

.

Therefore, the first ten terms of the sequence are .

Graph :

Graph the sequence .

Plot the first ten terms of the sequence are

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Observe the graph :

The sequence is approaches to the value .

Therefore, the limit value of the sequence is .

The sequence is  .

A sequence  is convergent, then there exist , where  is a constant.

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The sequence converges to .

The first ten terms of the sequence are .

Yes, the sequence have a limit and the value is .