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| PAGE: 630 | SET: Exercises | PROBLEM: 1 |
The series are 
, 
and 
.
(a)
, where 
.
, where 
.
, where 
.
Observe the corresponding values and identify the series:
.gif)
(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.
Compare 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.
Thus, the series converges.
(d) The smaller the magnitudes of the terms , the smaller the magnitudes of the terms of the sequence of partial sums.
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