The series are ,  and .

(a)

, where .

, where .

, where .

Observe the corresponding values and identify the series:

(b)

The series are ,  and .

The general form of - series is .

The series is converges if  and diverges if .

Observe the series.

The series  is in the form of - series.

Comapre the series with general form.

The series is converges because .

Therefore,  is converges.

(c)

The magnitudes of the terms are less than the magnitudes of the terms of the - series.

Therefore, the series converges.

(d)

The smaller the magnitudes of the terms , the smaller the magnitudes of the terms of the sequence of partial sums.

(a)

(b)  is converges.

(c) The magnitudes of the terms are less than the magnitudes of the terms of the - series.

Therefore, the series converges.

(d) The smaller the magnitudes of the terms , the smaller the magnitudes of the terms of the sequence of partial sums.