Q. 194.7( 3 Votes )

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

Answer :

In order to show that 9^{n+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,

9^{n+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, 9^{n+1} – 8n – 9 is divisible by 64.

Hence Proved.

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