Does the second hint mean that ln(1+x) approaches x/2 for x close to zero ?
Should the case for k + 1 partial sum eventually look like ((m+1)/(2*(m+1) + 1)) after some manipulation.
If so I'm having trouble getting to that end result.
I've sort of broken down and just resorted to the partial fractions method.
I'd still like to see the induction principle used on this challenge however.
Please forgive the humorous greeting, I couldn't help it, after not knowing that you were a faculty member for so long.
Professors are made fun of a lot however, so you may be used to it.
Thanks for those inspirational words.
I personally need something of that sort to keep chugging on with this stuff.
Thank you both.
I'll keep on keepin' on.
I also noticed in the help pages for the Dagger command that there was not an example of the command used specifically with a matrix of any type.
I was only able to find an explicit statement that matrices could be used.
Has anyone taken a look at this ?
Anything that you have so far would be
I can get the HermitianTranspose command to
work, but not Dagger.
Thanks for your procedure. After experimenting with it, it showed me that perfect numbers seem to be few and far between.
This also seems to be even more true when you go very far to the right the real number line.
Your suggestion gave the first few perfect numbers. However, why didn't Maple just provide a procedure that allows one to enter integers or a range of integers and test whether or not any perfect numbers are present ?
Also, what is the biggest integer one can use in the solution that you gave ?
I also had the same trouble with grasping that command the first time I saw it.
I think it is a bit of a misnomer, that I guess I just have to get accustomed to.
Is this the same thing as fourier analysis ?
In your link I think I saw about 5 different waves.
However, would summing a lot more different frequencies and amplitudes have created some arbitrary periodic waveform ?
Also, is the reason the example shown doesn't have any regularity to it is because there still are not enough waveforms included yet ?
In the text book I'm browsing through, "Intro to Quantum Mechanics", by David Griffiths, he simply has sin(theta) (table 4.1, page 127).
Why does simplify also have to be used after invoking the LegendreP function ?
Could the text be a misprint ?
Thanks to all.
I thought I would use this reply to inquire about anything on the post I made regarding the associated Legendre function.