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

  1. #1
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    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
    Can anyone please help me ?
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  2. #2
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    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.
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  4. #4
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    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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  5. #5
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    Thread closed due to this member deleting questions after getting help.
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