SOLUTION: How many terms are there in the expansion of (x-1/x)^18? Is there a term which is independent of x? Find this term if it exists. Also find the middle term in this expansion.

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Question 822118: How many terms are there in the expansion of (x-1/x)^18? Is there a term which is independent of x? Find this term if it exists. Also find the middle term in this expansion.

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


If there is a term independent of x, it will be a term when
the exponent of x is 0, since x0 = 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  = 48620

Note that  = 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

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