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

• Jul 12th 2010, 12:16 PM
jess0517
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
• Jul 12th 2010, 12:35 PM
chaoticmindsnsync
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.
• Jul 12th 2010, 12:41 PM
jess0517
.
• Jul 12th 2010, 12:45 PM
jess0517
Thanks soo much for the reply but thats actually where i got stuck.. trying to get 5^(k+1) from 5^(k+2). I split the terms to get 5^k and 5^2 but i couldnt figure out how to get the 5^(k+1) as needed from that =/.
• Jul 14th 2010, 02:30 AM
mr fantastic
Thread closed due to this member deleting questions after getting help.