Estimated Sums in Infinite Series Problem

Thread starter pjcircle
Start date Jan 30, 2013
Tags

Infinite Infinite series Series Sums

Jan 30, 2013

pjcircle

Homework Statement

How many terms of the series do we need to add in order to find the sum to the indicated accuracy?
Ʃ((-1)ⁿ)/(n(10ⁿ)) from n=1 to infinity
|error| <.0001

I keep ending up with n=log(4)-log(n)

Physics news on Phys.org

Jan 30, 2013

haruspex

Science Advisor

Homework Helper

Insights Author

Gold Member

2024 Award

Please post your working.

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

View full post »

Thread 'Solve this problem that involves induction'

Hello, This is the attachment, the steps to solution are pretty clear. I guess there is a mistake on the highlighted part that prompts this thread. Ought to be ##3^{n+1} (n+2)-6## and not ##3^n(n+2)-6##. Unless i missed something, on another note, i find the first method (induction) better than second one (method of differences).

View full post »