help? series?

Question

Answer 1

(1.a)

Step 1:

The sequence is .

Find the first five terms of the sequence.

First term of the sequence is .

Second term of the sequence is .

Third term of the sequence is .

Fourth term of the sequence is .

Fifth term of the sequence is .

Solution:

The first five terms of the sequence are , , , and .

Answer 2

(1.b)

Step 1:

The sequence is .

Find the first five terms of the sequence.

First term of the sequence is .

Second term of the sequence is .

Third term of the sequence is .

Fourth term of the sequence is .

Fifth term of the sequence is .

Solution:

The first five terms of the sequence , , , and .

Answer 3

(2)

Step 1:

The sequence is .

Consider .

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

As , then .

.

.

The sequence converges to .

Solution:

The sequence converges.

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