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Q.

For all n€ R, 9n+1 - 8n - 9 is divisible by

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a

64

b

63

c

62

d

65

answer is A.

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Detailed Solution

9n+1−8n−9=9n×9−8n−9=(1+8)n×9−8n−9= nC0+nC18+nC282+nC383+…+nCn8n9−8n−9=1+8n+nC282+nC383+…+nCn8n9−8n−9=9+72n+ nC282+nC383+…+nCn8n9−8n−9=(72n−8n)+82 nC2+nC38+…+nCn8n−29=64n+64 nC2+nC38+…+nCn8n−29=64n+ nC2+nC38+…+nCn8n−29= 64 x Some constant numbers= Divisible by 64

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