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 August 23rd, 2019, 02:12 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 642 Thanks: 91 Prove inequality Prove: $\displaystyle e^{n^2} \left(1^1 \cdot 2^2 \cdot 3^3 \cdot ...\cdot n^n \right)\leq n^{n^2 + n + 6}$. Last edited by skipjack; August 23rd, 2019 at 06:16 AM.
August 23rd, 2019, 09:35 AM   #2
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Quote:
 Originally Posted by idontknow Prove: $\displaystyle e^{n^2} \left(1^1 \cdot 2^2 \cdot 3^3 \cdot ...\cdot n^n \right)\leq n^{n^2 + n + 6}$.
For $\displaystyle n\neq 1$.

 August 23rd, 2019, 09:49 AM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 642 Thanks: 91 $\displaystyle e^{n^2 }(\underbrace{n^n •...•n^n }_{n} ) August 23rd, 2019, 09:49 AM #4 Math Team Joined: May 2013 From: The Astral plane Posts: 2,272 Thanks: 942 Math Focus: Wibbly wobbly timey-wimey stuff. Quote:  Originally Posted by idontknow For$\displaystyle n\neq 1\$.
Sounds like a mathematical induction problem. Can you set that up?

-Dan

 August 23rd, 2019, 01:18 PM #5 Global Moderator   Joined: Dec 2006 Posts: 20,972 Thanks: 2222 I've closed this thread as the original poster realizes he didn't get it right. Thanks from topsquark

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