From the following:
How to solve, N, fully (the above) ?
Thanks in advance for your time and help.
Solved! Go to Solution.
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
Note that you should not assume n>0, since n=0 gives 2*n+1=1, the first odd number.
Can maple prove it?
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:
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.
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.
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 .... ??