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Question
9n+1-8n-9 is divisible by 64
9n+1-8n-9 is divisible by 64
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Solution
The correct option is A True
It is given 9n+1 - 8n - 9 is divisible by 64.So we have to express the given terms in terms of 64 or the multiple of 64. We can write 9 as 8+1 and proceed.
9n+1−8n−9=(8+1)n+1−8n−9
(8+1)n+1−8n−9=(n+1C0(8)n+1+n+1C1(8)n+n+1C2(8)n−1+........n+1Cn−1(8)2+n+1Cn(8)+n+1Cn+1)−8n−9
(8+1)n+1−8n−9 = (Multiple of 64 + (n+1)(8) + 1) - 8n - 9
(8+1)n+1−8n−9 = (Multiple of 64 + 8n + 8 + 1) - 8n - 9
(8+1)n+1−8n−9 = Multiple of 64 + 8n + 9 - 8n - 9
(8+1)n+1−8n−9 = Multiple of 64
⇒ The statement is true
True
It is given 9n+1 - 8n - 9 is divisible by 64.So we have to express the given terms in terms of 64 or the multiple of 64. We can write 9 as 8+1 and proceed.
9n+1−8n−9=(8+1)n+1−8n−9
(8+1)n+1−8n−9=(n+1C0(8)n+1+n+1C1(8)n+n+1C2(8)n−1+........n+1Cn−1(8)2+n+1Cn(8)+n+1Cn+1)−8n−9
(8+1)n+1−8n−9 = (Multiple of 64 + (n+1)(8) + 1) - 8n - 9
(8+1)n+1−8n−9 = (Multiple of 64 + 8n + 8 + 1) - 8n - 9
(8+1)n+1−8n−9 = Multiple of 64 + 8n + 9 - 8n - 9
(8+1)n+1−8n−9 = Multiple of 64
⇒ The statement is true
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