The following product gives 0

restart;

product(1-1/k, k = 2 .. infinity);

                               0

However when I expand the product

1 - 1/2 - 1/3 - 1/4 - ... + 1/2*1/3 + 1/2*1/4 + ... + 1/3*1/4 + ... + triple products + quadruple products + and so forth...

Now the double, triple, quadruple, and so forth sums of products converge.

The 1/2 + 1/3 + 1/4 + ... nevertheless diverges, so why does maple give me 0?

Suppose I have a subset of R^2, say (x,y) € [0,1] x [0,1]

Now I map

x=r*exp(t)

y=r*exp(-t)

Is it possible to do a 2d contourplot to just see where [0,1]x[0,1] is mapped onto ?

I tried to integrate

int((1-x^floor(u))/((1-x)*u^2), u = 1 .. infinity, numeric)

where x=-1. The result should be log 2 = 0.6931471806. However it gives me 0.6687714032.

When using a numeric cut off, the result improves, so what is the issue here?

6687714032

In Physics package there is this compact notation X=(t,x,y,z)

Is there something similar in the VectorCalculus packge?

For example

restart;

with(VectorCalculus);

SetCoordinates(cartesian[x, y, z]);

v := VectorField([vx, vy, vz]);

Jacobian(v);

I don't explicitly want to write the arguments (x,y,z) of the functions vx,vy,vz everytime.

So I have this system of equations with which I am not sure if the result is the same or not using "series" and "limit" or what is going on here.

I hope it is clear what I mean.

Download Mapleprimes_-_Ionproduct.mw