n > sqrt(n) + n^1/3 + n^1/4, for n > 9

 
 
                                                          Difference

2 \; < \; \sqrt {2} \; + \; \sqrt[3]{2} \; + \; \sqrt[4]{2} ………. -1.86334

3 \; < \; \sqrt {3} \; + \; \sqrt[3]{3} \; + \; \sqrt[4]{3} ………. -1.49037

4 \; < \; \sqrt {4} \; + \; \sqrt[3]{4} \; + \; \sqrt[4]{4} ………. -1.00161

5 \; < \; \sqrt {5} \; + \; \sqrt[3]{5} \; + \; \sqrt[4]{5} ………. -0.441393

 

6 \; > \; \sqrt {6} \; + \; \sqrt[3]{6} \; + \; \sqrt[4]{6} ………. 0.168305

7 \; > \; \sqrt {7} \; + \; \sqrt[3]{7} \; + \; \sqrt[4]{7} ………. 0.814741

8 \; > \; \sqrt {8} \; + \; \sqrt[3]{8} \; + \; \sqrt[4]{8} ………. 1.48978

9 \; > \; \sqrt {9} \; + \; \sqrt[3]{9} \; + \; \sqrt[4]{9} ………. 2.18787

 
Prove that

n > \sqrt {n} \; + \; \sqrt[3]{n} \; + \; \sqrt[4]{n}   for all integers   n > 9

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Advertisements

About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s