How do you use the Binomial Theorem to expand #(1 + x) ^ -1#?

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Answer 1 · 2017-03-02T11:01:32

The answer is #=1-x+x^2-x^3+x^4+....#

The binomial series is

#(1+y)^n=sum_(k=0)^(oo)((n),(k))y^k#

#=1+ny+(n(n-1))/(2!)y^2+(n(n-1)(n-2))/(3!)y^3+.....#

Here, we have

#y=x#

#n=-1#

Therefore,

#(1+x)^(-1)=1+(-1)(x)+((-1)(-2))/(2!)(x)^2+((-1)(-2)(-3))/(3!)(x)^3+((-1)(-2)(-3)(-4))/(4!)(x)^4+.......#

#=1-x+x^2-x^3+x^4+....#