Paper 1 – Condition of Sum to Infinity

Example

6 The first three terms of an infinite geometric sequence are � , � 6 , � 6r , where r is the r common ratio . The two possible values of r are ³ 2 ^and 2

� . 3

( a ) State which value of r leads to this sum and justify your answer .

( b ) Hence , calculate the sum of the sequence .

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Solution

( a )

6

( b ) u1

��

( A1 ) for finding u

1

2 �

3 u � ( A1 ) for correct value

1

9 u1

S ^� �

1� r 9

S _�

� ( A1 ) for substitution

� 2 � 1� _� � _�

� 3 �

27

S _�

� A1 5

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