p >Hello. I'm still kind of new to the practice of using a computer program to manipulate equations. I knew that one way to define an ellipse is as the locus of points P such that for 2 fixed points F1 and F2 the sum PF1 + PF2 is constant. I also know that in Cartesian coordinates, we get a formula of the form Ax2 + By2 = 1. If we set up our coordinate system such that F1 and F2 are on the x axis each a distance c from the origin and the maximum width of the ellipse is 2a, let's try to figure out A and B using MAPLE.

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The other day I was doing some not so light recreational reading. On page 83 of GAMMA Julian Havil
discusses the Bernoulli numbers. Evidently there exists a set of numbers B(0), B(1), ... such that

sum(k^pwr,k=1..n) = (1/(pwr+1)) * sum((n^i) * B(pwr+1-i)* binomial(pwr+1,pwr+1 - i),i=1..pwr+1)

Havil listed the first 12 Bernoulli numbers B0, B1, ..... = 1 1/2 1/6 0 -1/30 0 1/42 0 -1/30 0 5/66 0, ...

He also stated that the Bernoulli numbers were part of the coefficients of the expansion of x / [ (exp(x) -1)]

Hello, I sent this letter to MAPLE tech support and they suggested that i post it here. After using MATHCAD for a number of years, I recently purchased MAPLE 10. I am really blown away by this software’s depth and versatility. I am particularly impressed by how well geared it is to do symbolic math, and by the fact that with MAPLE you can see the steps involved in a complicated symbolic integration. I do find however, that the price of MAPLE’s extra power is that it is less intuitive and has a steeper learning curve in comparison to MATHCAD. There is definitely one area in which I have found MATHCAD is superior to MAPLE. I realize that I may not be fair to MAPLE. There exists the possibility that one can do in MAPLE a certain thing I have been doing in MATHCAD and I just don’t know how to do it yet. It is that possibility which is behind this letter.