+0  
 
0
730
11
avatar+1314 

What is 2^2014 - 2^2013. Found at Brilliant.org (problem solving site)

If you can easily answer this, don't. You might prefer to check out the site and challenge your self if it is any good, leave some feed back. 

Stu  Jul 8, 2014

Best Answer 

 #2
avatar+92206 
+16

Zegroes, the best way to do this is to factor out the 2^2013 like this.....

 

$$2^{2014}-2^{2013}\\\\
=2^{2013}*2-2^{2013}\\\\
=2^{2013}(2-1)\\\\
=2^{2013}$$

This is a very large number. But it is not infinity.

Melody  Jul 8, 2014
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11+0 Answers

 #1
avatar+4150 
+8

Whats the definition of easy?Is it putting it in the calculator like this=2^2014- 2^2013 and getting the answer which i guess would be infinity?

zegroes  Jul 8, 2014
 #2
avatar+92206 
+16
Best Answer

Zegroes, the best way to do this is to factor out the 2^2013 like this.....

 

$$2^{2014}-2^{2013}\\\\
=2^{2013}*2-2^{2013}\\\\
=2^{2013}(2-1)\\\\
=2^{2013}$$

This is a very large number. But it is not infinity.

Melody  Jul 8, 2014
 #3
avatar+4150 
0

The calculator literally said infinity.

zegroes  Jul 8, 2014
 #4
avatar+92206 
0

Yes the calculator said that but that is only because it was too big to be displayed in any kind of conventional way.  It is not REALLY infinity!

Melody  Jul 8, 2014
 #5
avatar+26625 
+5

$$2^{2013}\approx9.4\times10^{605}$$

There are 606 digits in all.  This is what 22013 is in full:

2^2013

Alan  Jul 8, 2014
 #6
avatar+11847 
+6

Oh MY GOD! Seeing this Alan is making my head go round and round!

rosala  Jul 8, 2014
 #7
avatar+1314 
0

How does one arrive at the numerical value for the answer both by calculator and manually?

Stu  Jul 15, 2014
 #8
avatar+26625 
+8

I don't think standard calculators will give you 606 places of digits!  I used some computer software that has symbolic math capabilities.

You could do it by hand, in principle, just by starting with 2 and multiplying it by itself 2013 times.  Good luck with that!

Alan  Jul 15, 2014
 #10
avatar
0

I watched a trained chimpanzee tend a bar. He’d mix drinks to order and he’d light up a cigarette during a break. This was very funny to watch! He made good drinks too.

If a chimpanzee can tend a bar, you can probably learn how to do this, stu. This would be very funny to watch too!

However, if you can’t, give it to the chimp he probably can do it.

----

A chimp in time saves 2^2013

Guest Jul 15, 2014
 #11
avatar+1314 
0

.. YOu're a slow ****er Anon. Trolls have no brains. Good luck with that. You're post does not answer the question. No justification for question given. 


Stu  Jul 16, 2014
 #12
avatar
0

Sorry! Would you like a banana?

Guest Jul 16, 2014

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