The sequence is convergent.

, where is a finite number.

(a)

Prove that .

From definition of a limit sequence, for every , there exists a corresponding integer such that for , .

Choose such that it corresponding integer , and then all , .

Choose an , such that it correspondings to integer .

Since for all , .

By the definition , .

By the induction, the definition for also holds for and .

The sequence is convergent.

Since is convergent, , where is a finite number.

The first term of the sequence is and for .

.

The solutions of are

and .

Since all terms if the sequence are positive, the limit is positive.

.

(a) .

(b) .