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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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