Math
posted by Candice on .
Use mathematical induction to prove that 2^(3n)  3^n is divisible by 5 for all positive integers.
ThankS!

check for n=1
2^3  3^1 = 83 = 5
assume for k:
2^(3k)  3^k = 5m for some m
now plug in k+1
2^(3(k+1))  3^(k+1)
= 2^(3k+3)  3^(k+1)
= 2^3 * 2^(2k)  3*3^k
= 8*2^(3k)  3*3^k
= 3*2^(3k) + 5*2^(3k)  3*3^k
= 3(2^(3k)  3^k) + 5*2^(3k)
= 3(5m) + 5*2^(3k)
which is a multiple of 5.