# Math Help - Need help to prove 5^n+5 < 5^(n+1)

1. ## Need help to prove 5^n+5 < 5^(n+1)

Prove 5^n+5 < 5^(n+1) for al n elements of N
So i started this by using induction and used n=1 for my base case which i got 10<25 which is true. Then i assumed that 5^k+5<5(k+1) for all k elements of N and computed:

5(k+1)+5< 5^(k+1)+1
soo i tried to split the right side to (5^k)x(5^2) then i got stuck
2. Remember, your induction hypothesis is $5^k+5<5^{k+1}$. Now, you need to prove $5^{k+1}+5<5^{k+2}$. Since you started on the RHS, when you split it, it should resemble the RHS of the induction hypothesis. In otherwords, you should have a term with $5^{k+1}$ in it after you split $5^{k+2}$ into the product of two terms. The rest should follow quickly then.