A sum with irrational limits

romsek

Math Team
Sep 2015
2,773
1,552
USA
That result isn't correct. For n=5 the sum equals approximately 0.81, and your right hand side equals approximately 0.293

You could have checked that yourself.
 
Aug 2018
128
7
România
That result isn't correct. For n=5 the sum equals approximately 0.81, and your right hand side equals approximately 0.293

You could have checked that yourself.
Hello,

Attention!If the limits of the sum are irrationals and \(\displaystyle \sqrt{2} \leq k \leq \sqrt{5}\) , then how does the value of \(\displaystyle k\) vary?
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Four questions:
1) How many terms does he have \(\displaystyle \sum_{k=\sqrt{2}}^{\sqrt{2}} \frac{1}{k(k+1)}\)?
2) How many terms does he have \(\displaystyle \sum_{k=\sqrt{2}}^{\sqrt{3}} \frac{1}{k(k+1)}\)?
3) How many terms does he have \(\displaystyle \sum_{k=\sqrt{2}}^{\sqrt{4}} \frac{1}{k(k+1)}\)?
4) How many terms does he have \(\displaystyle \sum_{k=\sqrt{2}}^{\sqrt{5}} \frac{1}{k(k+1)}\)?
Thank you very much!

All the best,

Integrator
 
Last edited:

romsek

Math Team
Sep 2015
2,773
1,552
USA
I'm done. If you want to write up how to do sums with irrational indices that don't obey the common sense translation you said yes to in post #3 then have at it.
 
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Aug 2018
128
7
România
I'm done. If you want to write up how to do sums with irrational indices that don't obey the common sense translation you said yes to in post #3 then have at it.
Hello,

:oops:I was wrong!Thousands of apologies!:oops:I was thinking about the limits of the sum ....:rolleyes:If I didn't upset you too much, then I would like we continue the discussion.Thank you very much!

All the best,

Integrator