Q. 133.6( 71 Votes )
Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.
Answer :
In order to show that 9n+1 – 8n – 9 is divisible by 64,
we have to prove that
9 n+1 – 8n – 9 = 64 k, where k is some natural number
Now,
9n+1 = (1+8)n+1
We know that-
putting a =1, b = 8, and n = n+1
Hence,
Taking out (8)2 from right side, we get-
where 
is a natural number
Thus, 9n+1 – 8n – 9 is divisible by 64.
Hence Proved.
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