What are the first 4 terms

Question

Find the first three non-zero terms of the Maclaurin series for f(x)=ln(1−x⁵)

Answer 1

Find the first three non-zero terms of the Maclaurin series for f(x)=ln(1−x⁵)

f(x)=ln(1−x⁵) = - ∫[5x⁴] / [ 1- x⁵ ] dx = - 5 ∫x⁴ [ 1+ x⁵ + x¹⁰ + x¹⁵ + x²⁰ +···] dx =

= - 5 ∫ [ x⁴ + x⁹ + x¹⁴ + x¹⁹ +....] dx = -5 [ x⁵/5 + x¹⁰/ 10 + x¹⁵/15 + x²⁰ /20 + ....] =

= - [ x⁵ + x¹⁰/ 2 + x¹⁵/3 + x²⁰ /4 + ....] =

= - ∑_n=1 x⁵ⁿ/n