# Thread: Is this induction correct/?

2. ## Re: Is this induction correct/?

Here is a list of $k!$ for $k=0,1,2,3,4,5,6,7$

$\{1,1,2,6,24,120,720,5040\}$

and a list of $3^k$ for $k=0,1,2,3,4,5,6,7$

$\{1,3,9,27,81,243,729,2187\}$

3. ## Re: Is this induction correct/?

so there is something wrong with your induction proof

4. ## Re: Is this induction correct/?

But isn't that what I did? I expressed (k+1)! in terms of 3^(k+1)

so I essentially showed that 3k! is greater than or equal to 3^(k+1).. which is correct, no?

5. ## Re: Is this induction correct/? Originally Posted by math951 But isn't that what I did? I expressed (k+1)! in terms of 3^(k+1)
so I essentially showed that 3k! is greater than or equal to 3^(k+1).. which is correct, no?
Look at this calculation.
It appears that your base case is off.
So if $n\ge 7$ then $n!>3^n$.

6. ## Re: Is this induction correct/?

Okay I see...so the whole point was is that they wanted me to find the integer where the inequality holds true.