Question 822118
<pre>{{{(x-1/x)^18}}}{{{""=""}}}{{{sum((matrix(2,1,18,k))*

(x^k*(1/x)^(18-k)),k=0,18)}}}{{{""=""}}}{{{sum((matrix(2,1,18,k))*(x^k*(x/1)^(-18+k)),k=0,18)}}}{{{""=""}}}{{{sum((matrix(2,1,18,k))*(x^k*x^(-18+k)),k=0,18)}}}{{{""=""}}}{{{sum((matrix(2,1,18,k))*(x^(2k-18)),k=0,18)}}}

If there is a term independent of x, it will be a term when
the exponent of x is 0, since x<sup>0</sup> = 1

So we set the exponent of x equal to zero:

2k-18 = 0
   2k = 18
    k = 9

So the term when k=9 is {{{(matrix(2,1,18,9))x^(2*9-18)}}}{{{""=""}}}{{{(matrix(2,1,18,9))x^0}}}{{{""=""}}}{{{(matrix(2,1,18,9))(1)}}}{{{""=""}}}{{{(matrix(2,1,18,9))}}} = 48620

Note that {{{(matrix(2,1,n,k))}}} = C(n,k) = nCk

Since the terms go k=0 to k=18, there are 19 terms and the middle
term will be the 10th term and that is when k=9.  Therefore the term
48620 IS the middle term.

Edwin</pre>