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

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Feb 2010
15
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Canada
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
Can anyone please help me ?
 
Jul 2010
9
4
Remember, your induction hypothesis is \(\displaystyle 5^k+5<5^{k+1}\). Now, you need to prove \(\displaystyle 5^{k+1}+5<5^{k+2}\). 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 \(\displaystyle 5^{k+1}\) in it after you split \(\displaystyle 5^{k+2}\) into the product of two terms. The rest should follow quickly then.
 
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Feb 2010
15
0
Canada
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 =/.
 

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Thread closed due to this member deleting questions after getting help.
 
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