SOLUTION: Expand. ( 2 + x )^(-4) where |x|>2

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Question 1091635: Expand. ( 2 + x )^(-4) where |x|>2
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

We will use the fact that

%281%2By%29%5E%28-n%29%22%22=%22%22sum%28%28-1%29%5Ek%2A%28matrix%282%2C1%2Cn%2Bk-1%2Ck%29%29y%5Ek%2Ck=0%2Cinfinity%29 converges for abs%28y%29%3C1,

and where %28matrix%282%2C1%2Cp%2Cq%29%29 is the number of combinations
of p things taken q at a time or p%21%2F%28q%21%28p-q%29%21%29

%282%2Bx%29%5E%28-4%29%22%22=%22%22%28x%2B2%29%5E%28-4%29%22%22=%22%22%28x%281%2B2%2Fx%29%5E%22%22%29%5E%28-4%29%22%22=%22%22x%5E%28-4%29%281%2B2%2Fx%29%5E%28-4%29%22%22=%22%22

 converges for abs%282%2Fx%29%3C1

Simplifying,

 converges for abs%28x%2F2%29%3E1

 converges for abs%28x%29%3E2

 converges for abs%28x%29%3E2

 converges for abs%28x%29%3E2

Edwin