20-Turquoise

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.

Best answer by LucMeekes

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

should give: N is odd.

Success!
Luc

25-Diamond I

Isn't the solution N = infinite ?

Answer

23-Emerald IV

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

should give: N is odd.

Success!
Luc

25-Diamond I

@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:

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

23-Emerald IV

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:

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

The command simplify:

Doesn't simplify, but simplify, max:

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:

Luc

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