Evaluate the limit:

**Solution**

It is quite known that

Thus,

Therefore, by induction , for ,

Summing the last equation we get:

and raising the last equation to the power , we get:

Thus, by the squeeze theorem the limit is equal to .

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Evaluate the limit:

**Solution**

It is quite known that

Thus,

Therefore, by induction , for ,

Summing the last equation we get:

and raising the last equation to the power , we get:

Thus, by the squeeze theorem the limit is equal to .