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lvl10720-Turquoise
20-Turquoise
October 4, 2022
Solved

Solve, N, fully ?

Hi, Everyone.
From the following:

solve, N, fully.PNG

 

How to solve, N, fully (the above) ?


Thanks in advance for your time and help.
Best Regards.
Loi.

LucMeekesAnswer
23-Emerald IV
October 5, 2022

LucMeekes_0-1664978213253.png

I'd say: Fun(N)=1, solve, N, fully

should give: N is odd.

 

Success!
Luc

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8 replies

Werner_E
Werner_E25-Diamond I
25-Diamond I
October 4, 2022

Isn't the solution N = infinite ?

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LucMeekes23-Emerald IVAnswer
23-Emerald IV
October 5, 2022

LucMeekes_0-1664978213253.png

I'd say: Fun(N)=1, solve, N, fully

should give: N is odd.

 

Success!
Luc

Translate
    Werner_E
    Werner_E25-Diamond I
    25-Diamond I
    October 5, 2022
    @LucMeekes wrote:

     

    I'd say: Fun(N)=1, solve, N, fully

    should give: N is odd.

    I agree. My assumption N=infinity was grossly incomplete 😉

     

    Is Maple in MC11 able to prove it? muPad in MC15 isn't:

    Werner_E_1-1664980516811.png

    Problem is the first summand in Fun(N) (Mathcad changes the order in the result) as already seen here: https://community.ptc.com/t5/Mathcad/Sum-of-reciprocals/m-p/827578/highlight/true#M202986

     

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    LucMeekes23-Emerald IV
    23-Emerald IV
    October 7, 2022

    Note that you should not assume n>0, since n=0 gives 2*n+1=1, the first odd number.

    Can maple prove it?

    Let's try:

    LucMeekes_0-1665137157170.png

    That's equivalent to MuPad's result. Setting n to a n integer:

    LucMeekes_1-1665137204240.png

    The command simplify:

    LucMeekes_3-1665137312015.png

    Doesn't simplify, but simplify, max:

    LucMeekes_4-1665137433530.png

    creates a different result, I've never seen simplify, max create a different result from simply simplify in Mathcad 11.

    But then again, simplify, simpler  creates that very same result:

    LucMeekes_6-1665137591713.png

     

    Luc

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