Question

Question #a8879

Answer 1

A formula to memorize is the MacLaurin series of `ln(1+x)`.

`ln(1+x)=sum_(n=0)^(oo)frac{(-1)^n(x)^(n+1)}{n+1}`

Therefore:
`ln(1+4x)=sum_(n=0)^oofrac{(-1)^n(4x)^(n+1)}{n+1}`

`=sum_(n=0)^oofrac{(-1)^n(4)^(n+1)(x)^(n+1)}{n+1}`