Solve, N, fully ?

[lvl107]

Hi, Everyone.
From the following:

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

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

[Werner_E]

Isn't the solution N = infinite ?

[LucMeekes · Accepted solution]

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

should give: N is odd.

Success!
Luc

[Werner_E]

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@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

[LucMeekes]

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

[Werner_E]

In MC14/15 "simplify,max" often makes a difference, but apart from taking much more time it also sometimes returns a result which is even worse compared to the one we get with "simplify" alone.

BTW, "simplify,simpler" throws the error "Modifier is unknown or not allowed here" in MC15.

[LucMeekes]

Mathcad 11 doesn't know that error message. It allows anything as a modifier for simplify. But it's striking to see that an absent modifier gives a (slightly but) different result from a non-empty modifier.

Luc

[lvl107]

Many thanks, Luc and Werner.

Luc, with your suggestion above, And I agree with you, too:

    

Best Regards.

Loi.

[Werner_E]

Here is a list for the first few N showing N, the reduced first an second summand and the complete sum.

Some sort of pattern can be seen, but the proof is .... ??