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dj so orz
by
Yiyj1, Mar 29, 2025, 1:42 AM
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legendary problem writer
by
Clew28, Jul 29, 2024, 7:20 PM
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orz
by
balllightning37, Jul 26, 2024, 1:05 AM
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hi dj
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OronSH, Jul 23, 2024, 2:14 AM
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i wanna submit my own problems lol
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ethanzhang1001, Jul 20, 2024, 9:54 PM
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hi dj, may i have the role of contributer?
by
lpieleanu, Feb 23, 2024, 1:31 AM
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This was helpful!
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YIYI-JP, Nov 23, 2023, 12:42 PM
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waiting for a recap of your amc proposals for this year
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ihatemath123, Feb 17, 2023, 3:18 PM
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also happy late bday man! i missed it by 2 days but hope you are enjoyed it
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ab456, Dec 30, 2022, 10:58 AM
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Contrib?
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MC413551, Nov 20, 2022, 10:48 PM
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tfw kakuro appears on amc
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bissue, Aug 18, 2022, 4:32 PM
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Hi dj
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799786, Aug 10, 2022, 1:44 AM
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Roses are red,
Wolfram is banned,
The best problem writer is
Djmathman
by
ihatemath123, Aug 6, 2022, 12:19 AM
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hello
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aidan0626, Jul 26, 2022, 5:49 PM
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Do you have a link to your main blog that you started after graduating from high school, I couldn't find it. @dj I met you IRL at Awesome Math summer Program several years ago.
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First, Mar 1, 2022, 5:18 PM
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how did you do that cursor
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mathgenius64, Sep 1, 2011, 10:14 PM
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Finally posted that problem! And hooray for pencil cursor!
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djmathman, Aug 24, 2011, 6:49 PM
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Geo 2 is correct though
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sjaelee, Aug 24, 2011, 12:21 AM
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Hello...Lol yesterday sjaelee posted Geomretry #2. Isn't it supposed to be Geometry #2? Lol.
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mcqueen, Aug 23, 2011, 11:57 PM
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Delete geo #4! Plese!
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sjaelee, Aug 22, 2011, 11:41 PM
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Hrm, there's this problem that I've been too lazy to post. I think I should soon.
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djmathman, Aug 22, 2011, 7:02 PM
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Why hello...funny I'm saying this when I know you'll be unresponsive because you're V/LA for a week.
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mcqueen, Aug 14, 2011, 10:47 AM
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But that's because those problems are the easiest to find.
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djmathman, Aug 12, 2011, 3:49 AM
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Yea, I kind of keep forgetting to change that.
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djmathman, Aug 11, 2011, 11:27 AM
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I noticed that only algebra and number theory come up
(trig was basically algebra)
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sjaelee, Aug 11, 2011, 11:22 AM
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There you go.
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djmathman, Aug 7, 2011, 2:07 PM
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*cough* contrib
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Mrdavid445, Aug 7, 2011, 12:40 PM
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Ah, i'm sure you will use this blog well.
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tc1729, Aug 7, 2011, 2:10 AM
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First shout!
by
djmathman, Aug 5, 2011, 6:58 PM
by sjaelee, Sep 24, 2011, 3:11 PM ![\[ \left\lfloor 1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\dots+\frac{1}{\sqrt{1000000}}\right\rfloor. \]](//latex.artofproblemsolving.com/2/2/8/2280a78f0114ee09be88c236c3da59804f2e2452.png)
![\[ \left\lfloor 1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\dots+\frac{1}{\sqrt{1000000}}\right\rfloor. \]](http://latex.artofproblemsolving.com/2/2/8/2280a78f0114ee09be88c236c3da59804f2e2452.png)
![\[\sum_{k=1}^{n}\frac{1}{\sqrt{k}+\sqrt{k+1}}\]](http://latex.artofproblemsolving.com/e/9/c/e9c5e3906b74996921ce7c7a06d945a44ff31086.png)
![\[\sqrt{k+1}-\sqrt{k}\]](http://latex.artofproblemsolving.com/1/f/e/1fed15b1e843a77a5ecb77b6fa64cd27b9fbab7c.png)
)![\[\sqrt{1000001}-1\]](http://latex.artofproblemsolving.com/8/9/1/89193856d4b979f6f440f2c7cbe94ca28405f080.png)
. Multiplying 2, we have a number 
such that
. We know our desired is greater.![\[ 1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}< 2\sqrt{n} \]](http://latex.artofproblemsolving.com/e/5/5/e552c53ccc194a32a06d4c6f029ca2dd899e2ef9.png)
,
,
.
.![\[1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}<2\sqrt{n}\]](http://latex.artofproblemsolving.com/c/c/4/cc4dd8b5229a23964b86a38f1ca96085e61aab3e.png)
,![\[2\sqrt{n+1}>2\sqrt{n}+\frac{1}{\sqrt{n+1}}>
1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n+1}}\]](http://latex.artofproblemsolving.com/6/a/f/6af598e40b58904253a265b3b7bef3d738b0c878.png)
![\[2\sqrt{n+1}>2\sqrt{n}+\frac{1}{\sqrt{n+1}}\]](http://latex.artofproblemsolving.com/8/7/6/876e9e895dedc670f8aaf75485068c5462ba1b65.png)
to get
and 
.
and 
.
is
and 
.
that![\[ 1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}< 2\sqrt{n}-1 \]](http://latex.artofproblemsolving.com/6/c/2/6c256e62cb0146f8ca4de769ba42787f4ee3f4e5.png)
works.
. Thus, our desired, 
,
. Thus, our greatest integer is
.
April 2025
November 2024