Homework Help: Pre-calculus

Posted by Lucy on Monday, October 13, 2008 at 11:55am.

Which of the following series is divergent?

a) 1+3(1/4)+9(1/4)^2+27(1/4)^3...

b) 1+3(1/5)+9(1/5)^2+27(1/5)^3...

c) 1+3(1/7)+9(1/7)^2+27(1/7)^3...

d) 1+3(1/2)+9(1/2)^2+27(1/2)^3...

How do you determine if a series in convergent or divergent???

The book that I have is about as clear as mud and I do not understand...

Thanks for your help!!

Pre-calculus - Reiny, Monday, October 13, 2008 at 12:23pm
This would be a lengthy reply, so see if you can make sense out of this

http://faculty.msmary.edu/heinold/m248spring2007/m248spring2007_convergence_tests.pdf

I will take a look at the first question

1+3(1/4)+9(1/4)^2+27(1/4)^3...
= 1 + 3^1 / 4^1 + 3^2 / 4^2 + ..

= 1 + summation of (3/4)^n as n goes from 1 to infinitity

Now compare this result with what it says about the summation of a geometric series at the top of the link I gave you.

good luck.

Answer this Question

Related Questions

Pre Cal. - Find three geometric means betwee -sqrt(2) and -4sqrt(2). A: 2, -...
math-matrix equations - I have a problem with the following homework question: ...
Algebra - Factor: 3x^2 - 27 3x^2-27=0 27+(3x^2-27)=0+27 3x^2=27 (3x^2)/3=27/3 x^...
calculus - is this correct? use the integral test to determine if this series is...
calculus - f(x,y)=x^2+2y^2 use the gradient vector Þf(5, 1) to find ...
math - determine the difference between the sum of the infinite geometric series...
Pre-Calculus - I need help-I do not understand. The question is this: Write 2x+y...
College Calculus - Suppose the series An (from n=1 to INF) is known to be ...
math - consider the right traingel with sices 3, 4, and 5. the lengths form an ...
calculus - Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3...

For Further Reading

First Name:
School Subject:
Answer: