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Question

If 1+r+r2+...+rn= (1+r)(1+r2)(1+r4)(1+r8), then the value of n is

A
13
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B
14
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C
15
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D
16
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Solution

The correct options are
A 13
D 16
1+r+r2+........+rn=(1+r)(1+r2)(1+r4)(1+r8)
or(1rn1r)=(1+r)(1+r2)(1+r4)(1+r8)
or1rn=(1r)(1+r)(1+r2)(1+r4)(1+r8)
1rn=(1r2)(1+r2)(1+r4)(1+r8)
1rn=(1r4)(1+r4)(1+r8)(1rn)=(1r8)(1+r8)
1rn=1r16n=16

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