Hi,
Could someone help me solve this, please.
Show by Induction that for n >= 1:
(3^(3n)) + (2^(n+2)) is divisible by 5
Thanks.
True for n = 1.
Assume true for n = k.
Show that under the assumption it's true for n = k + 1:
$\displaystyle 3^{3(k+1)} + 2^{(k+1)+2} = 3^{3k} \cdot 3^3 + 2 \cdot 2^{k+2} = 27 \cdot 3^{3k} + 2 \cdot 2^{k+2}$
$\displaystyle = 25 \cdot 3^{3k} + 2 \cdot 3^{3k} + 2 \cdot 2^{k+2} = 25 \cdot 3^{3k} + 2 \left( 3^{3k} + 2^{k+2} \right)$
and it should be clear how to finish things off.