Alan

I assume this is a 50 gm bar of chocolate with 30% cocoa, in which case there are 0.3*50 = 15 gm cocoa.

Can also be done as follows:

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The denominator varies between 1 and 3  (finite positive numbers).  The numerator tends to infinity.  Infinity divided by any finite number is still infinite.

The result is indeed e/(2lambda):

Guest is correct, see more detail below:

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The following might be more helpful.  Put the result of one iteration into the expression symboloically, and then expand as a Taylor series:

It doesn't always converge to pi.  Try a value for n greater than 2pi for example.  And sometimes it takes a while to get going even when it does converge to pi.  or example, here's a graph where n = 2pi-10^-8

In general, the half life, L,  and the constant k are related by k = -ln(2)/L, so k = -ln(2)/5700 per year = 1.216*10^-4, as Guest has determined in the previous reply.

I assume i and j are unit vectors in the x- and y-directions respectively and that a dot product is required for v.w.

If so, then i.i = i, j.j = j and i.j = j.i = 0  so:

(3i + 5j)(-2i + 2/3j) =   -6i.i + 2i.j - 10j.i +10/3j.j   =  -6i + 10/3j

If v*w is meant to be a cross product (vxw) then the third, z, dimension is involved and 

ixi = jxj = kxk = 0

ixj = -jxi = k

jxk = -kxj = i

kxi = -ixk = j

This is undefined.