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- #1

- Feb 14, 2012

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$\sqrt[3]{\dfrac{2}{1}}+\sqrt[3]{\dfrac{3}{2}}+\cdots+\sqrt[3]{\dfrac{996}{995}}-\dfrac{1989}{2}<\dfrac{1}{3}+\dfrac{1}{6}+\cdots+ \dfrac{1}{8961}$

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- Thread starter
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- #1

- Feb 14, 2012

- 3,756

$\sqrt[3]{\dfrac{2}{1}}+\sqrt[3]{\dfrac{3}{2}}+\cdots+\sqrt[3]{\dfrac{996}{995}}-\dfrac{1989}{2}<\dfrac{1}{3}+\dfrac{1}{6}+\cdots+ \dfrac{1}{8961}$

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- #2

- Feb 7, 2012

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Not a solution, but a possible line of approach:

$\sqrt[3]{\dfrac{2}{1}}+\sqrt[3]{\dfrac{3}{2}}+\cdots+\sqrt[3]{\dfrac{996}{995}}-\dfrac{1989}{2}<\dfrac{1}{3}+\dfrac{1}{6}+\cdots+ \dfrac{1}{8961}$

Edit, Oh, it's suddenly obvious!

Last edited:

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- #3

- Feb 14, 2012

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That is a good line with all excellent observations,Not a solution, but a possible line of approach:

I can't wait to read your solution...Edit, Oh, it's suddenly obvious!

It's just an AM-GM argument – details to follow tomorrow.

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- #4

- Feb 7, 2012

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Previous comment now edited to complete solution.I can't wait to read your solution...

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- #5

- Feb 14, 2012

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Bravo,Edit, Oh, it's suddenly obvious!