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Help with symbolic calculation

SOLVED
rhanet
Regular Member

Help with symbolic calculation

I have tried to solve this summation with symbolic calculation but it does not give me an answer:

cálculo simbólico 1.jpg

If I give a value to n, I get an answer:

cálculo simbólico 2.jpg

Which keyword or modifier should I use to get a response without giving a numeric value to n??

Would appreciate any help to solve this problem.

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1 ACCEPTED SOLUTION

Accepted Solutions

Re: Help with symbolic calculation

Yes, the simplification is correct but Mathcad's abilities are unfortunately very limited when it comes to symbolic calculations. Especially when compared to more advanced systems like Mathematica or Maple or even whem compared to Uncle Wolfram (limited mathematica engine):

B4.PNG

I am surprised that even Luc did not succeed as he is using mathcad 11 which includes an older version of Maple to do the symbolic calculations.

 

View solution in original post

7 REPLIES 7

Re: Help with symbolic calculation

What would you want the solver to show for the generic n?  This?

tan(x) + tan(x/2)/2 + tan(x/4)/4 + tan(x/8)/8 + ... + tan(x/2^n)/2^n

This is beter shown with the sigma summation -- as in the original equation.

rhanet
Regular Member
(in response to MJG)

Re: Help with symbolic calculation

You're right, but what I want is to come up with a simplified summation result like this:

cálculo simbólico 3.jpg

For this I manually use this property:

cálculo simbólico 4.jpg

How can I implement it to get the desired result??

 

Re: Help with symbolic calculation

I'm afraid you will not succeed.

 

LM_20170914_Symbolic.png

Where did the summation go to?

 

Success!
Luc

Re: Help with symbolic calculation

After playing with the two equations provided by rhanet, I believe that the simplification is accurate.  I just can't find a way to make Matchad show it.  I can't get Mathcad to show that the innequality is true even if I include an assumption that n is an integer >= 0.

Re: Help with symbolic calculation

Yes, the simplification is correct but Mathcad's abilities are unfortunately very limited when it comes to symbolic calculations. Especially when compared to more advanced systems like Mathematica or Maple or even whem compared to Uncle Wolfram (limited mathematica engine):

B4.PNG

I am surprised that even Luc did not succeed as he is using mathcad 11 which includes an older version of Maple to do the symbolic calculations.

 

View solution in original post

Re: Help with symbolic calculation

I arrive at the answer giving values to n:

cálculo simbólico 5.jpg

generalizing we have:

cálculo simbólico 3.jpg

As werner says I will have to go to other programs to do this kind of symbolic calculations.

Thanks for the help.

Re: Help with symbolic calculation

Ah,  while the old Mathcad is in many ways more powerful than its successors, it has its limitations.

Exploring a little further:

LM_20170914_tan&cotsum0.png

LM_20170914_tan&cotsum1.png

Apparently the Maple engine runs astray for n=6, but a step-by-step analysis shows it stil should be able to arrive at the correct answers.

What exactly goes wrong for n= 6  and higher eludes me.

 

Luc

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