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$The remainder when 2^{0} + 2^{1} + 2^{2} + 2^{3} + \dots \dots + 2^{2014} is divided by 9 is$

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a

7

b

8

c

4

d

3

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detailed solution

Correct option is C

Consider, 20+21+22+23+…….+22014=122015−12−1=22015−1 ∵ In G.P series Sn=arn−1r−1=2223671−1=4(9−1)671−1=4(9λ−1)−1,λ∈ℝ=4(9λ)−5=4(9λ)−9+4=9(4λ−1)+4Since it is divided by 9, then reminder is 4.Therefore, the correct answer is (3).

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