Question

Find the maclaurin series of the given function f(x)=ln(1-x)

Answer 1

`-a-(a^2)/(2)-(a^3)/(3)-(a^4)/(4)-...-(a^n)/(n)-...`

Explanation:

1) the rule is:

`ln(1+a)=a-(a^2)/(2)+(a^3)/(3)-(a^4)/(4)+...+(-1)^(n-1)(a^n)/(n)+...`

2) according to the rule above:

`ln(1+(-a))=(-a)-((-a)^2)/(2)+((-a)^3)/(3)-((-a)^4)/(4)+...+(-1)^(n-1)((-a)^n)/(n)+...`

finally,

`ln(1-a)=-a-(a^2)/(2)-(a^3)/(3)-(a^4)/(4)-...-(a^n)/(n)-...`