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| PAGE: 736 | SET: Exercises | PROBLEM: 49 |
The value of 
.
(a)
Multiply each side by 
.
Substitute .
.
Threfore, the value is .
(b) Find the sum of the geometric series for the value of the .
Expand the value .
The general form of geometric series is 
.
Comapre the expression with general form.
The initial term is 
and the common ratio is 
.
The sum of the 
terms is 
.
Substitute 
and 
.
.
Therefore, the sum of the series is 
.
(c) Find the number of decimal representations of the integer number 
.
The value is .
Rewrite the value .
The value of 
.
The valus of 
and 
are the same.
Therefore, the number one has 
number of decimal representations.
(d) Find the numbers have more than one decimal representations.
Except the number 
, all the rational numbers have more than one decimal representation.
Hence all the rational numbers with a terminating decimal representation, except 
.
(a) The value is .
(b) The sum of the series is .
(c) The number one has 
number of decimal representations.
(d) Except the number , all the rational numbers have more than one decimal representation.
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