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| PAGE: 670 | SET: Exercises | PROBLEM: 78 |
The series is 
and the interval is 
.
(a)
Find the sum of the series when 
.
Substitute 
in 
.
.
The series is in the form of geometric series.
The general form of geometric series is 
.
The sum of the geometric series is 
.
Compare the series with general form.
Here 
and 
.
The sum of the series is 
.
Graph :
Graph the first six terms of the series and the sum of the series 
.
(b)
Find the sum of the series when 
.
Substitute 
in .
The series is in the form of geometric series.
The general form of geometric series is 
.
The sum of the geometric series is 
.
Compare the series with general form.
Here 
and 
.
The sum of the series is 
.
Graph :
Graph the first six terms of the series for .
.gif)
(c)
The series is converges for because it is an alternating series.
Observe the graph that for partial sums approach sum of series from below the sum of the series but for partial sums alternate around solution.
(d)
The partial sum is 
.
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(a) Graph :
Graph the first six terms of the series for 
.
(b) Graph :
Graph the first six terms of the series for 
.
(c) The series is converges for because it is an alternating series.
Observe the graph that for partial sums approach sum of series from below the sum of the series but for partial sums alternate around solution.
(d)
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