Q19 of 26 Page 8

Show that 9n+1 – 8n – 9 is divisible by 64, whenever n is a positive integer.

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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