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

Question

269214 views around the world

You can reuse this answer
Creative Commons License

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,

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

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

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