Express f(x) = ln(x+1) as an infinite series in ascending powers of x up to the 3rd power of x

Recall that the Maclaurin series for f(x) is f(x) = f(0) + f'(0)x + f''(0)x2/2! + ... + f(r)(0)xr/r! + ... Here f(0) = ln(1+0) = ln1 = 0 , f'(x) = 1/(1+x) using the chain rule. f'(0) = 1/1 = 1 , f''(x) = -1/(1+x)2 , f''(0) = -1/(1)2 = -1 , f'''(x) = 2/(1+x)3 , f'''(0) = 2/(1)3 = 2, Substituting these into the general expression for the Maclaurin series: (to 3rd degree) gives: ln(1+x) = 0 + 1x + -1/2! x2 + 2/3! x3 , ln(1+x) = x - x2/2 + x3/3

Related Further Mathematics A Level answers

All answers ▸

Using the definitions of hyperbolic functions in terms of exponentials show that sech^2(x) = 1-tanh^2(x)


A=[5k,3k-1;-3,k+1] where k is a real constant. Given that A is singular, find all the possible values of k.


Find the determinant of a 3x3 square matrix


Further Maths: How do you find the inverse of a 2 x 2 matrix?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences