Question

Prove that 5^2n -6n+8 is divisible by 9 for all positive integers n

Answer 1

Answer:

Step-by-step explanation:

let P(n):2  

n

>n

When n=1,2  

1

>1.Hence P(1) is true.

Assume that P(k) is true for any positive integer k,i.e.,

2  

k

>k  

we shall now prove that P(k+1) is true whenever P(k) is true.

Multiplying both sides of (1) by 2, we get

2.2  

k

>2k

i.e., 2  

k+1

>2k

k+k>k+1

∴2  

k+1

>k+1