Question

If |x|<1 ,the coefficient of x 3 in the expansion of 1/(e x.(1x)) is

Answer 1

1ex(1+x)=e−x(1+x)−1We know that e−x=1−x1!+x22!−x33!+x44!−....and(1+x)−1=1+x+x2+x3+...⇒e−x(1+x)−1=[1−x1!+x22!−x33!+x44!−....][1+x+x2+x3+...]=1−1+12!−13!=12−16=3−16=13

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