14 июл. 2023 г. · Question: 3. Find a power series for ln(1+5x2) and determine its interval of convergence. student submitted image, transcription available below.

8 дек. 2015 г. · It ends up equaling 1−12+13−14+⋯ , which is the so-called Alternating Harmonic Series, which converges (though not "absolutely").

29 мар. 2017 г. · From (a), f(x)=ln(1+x)=∞∑n=1(−1)n−1(xn)n. Then, (c) becomes ln(x2+1)=ln(1+x2)=f(x2)=∞∑n=1(−1)n−1(x2n)n. ln(1+x)$ -- why does its power series converge for $|x| < 1 What is the correct radius of convergence for $\ln(1+x) Finding the power series of a logarithmic function. Why does the taylor series of $\ln (1 + x)$ only approximate it for Другие результаты с сайта math.stackexchange.com

Продолжительность: 14:32
Опубликовано: 28 мар. 2021 г.

Substitute the series for ln(1+t^2) and integrate term-by-term to get x^3/3-x^5/10+x^7/21-x^9/36+cdots. The radius of convergence is 1. The Taylor series ...

30 июл. 2019 г. · To find the power series for ln(1 - x) you: •derive the power series for the function: 1/(1 - x) •integrate to find the power series for ln(1 - ...

Продолжительность: 8:45
Опубликовано: 11 апр. 2021 г.

16 нояб. 2022 г. · In this section we discuss how the formula for a convergent Geometric Series can be used to represent some functions as power series.

Продолжительность: 3:30
Опубликовано: 8 апр. 2021 г.

d) How many terms of the infinite series from' part c) need to be added to approximate the integral accurately to within 10-6? Use the Alternating.