CALC II
posted by Ace .
Determine the convergence of the following series using the nthpartial sum or geometric series formula.
The sum of n=1 to inifitiy 1/(9n^2+3n2)
How do I start? I'm guessing I should factor out the denominator but whats after that?
It is close to a geometric series, so use that test: the ratio of sucessive terms.
ratio= (9n^2+3n2)/(9(n+1)^2 + 3(n+1) + 2)
and show it is less than one.
if it is geometric what is the sum of n?
Respond to this Question
Similar Questions

Algebra
Use the geometric sequence of numbers 1, 1/3, 1/9, 1/27… to find the following: Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? 
Math....Please help I have a deadline for tonight!
Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following: b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? 
sum geometric series
what is the sum of geometric infinite series 3/2+ 9/16+ 27/128+ 81/1024=.... i know the formula is S=a/(1r) my teacher, he usually transforms into a formula of the sum series and finds out a and r.but i don't how to do that. the pattern … 
calc.
find the sum of the series of (2)^n/3^n+1. This is an alternating series... what if we rewrite it as an= (1/3)* (2/3)^(n) Divide any nth term by the n1 term and see if you get a ratio term r. This might be a geometric series. 
Math
I have a couple questions about the sums of geometric series. One. So the formula for the sum is t(n)=t(1)[(r^n)1] But if my series starts at t(0), can I change the formula to t(n)=t(0)[(r^n)1] ? 
Calc
We are working on finding the intervals of convergence of power series in class. Why do we not have to test for the convergence of the endpoints for geometric series? 
Calc II
Use the comparison or limit comparison test to decide if the following series converge. Series from n=1 to infinity of (4sin n) / ((n^2)+1) and the series from n=1 to infinity of (4sin n) / ((2^n) +1). For each series which converges, … 
CALC 2
a. Consider the following limit as a fact: lim n> infinity ((n!)^1/n)/n = 1/e Use this limit to study the convergence of this series using the root test. Sum of infinity and n=1 of ((3^n)n!)/n^n b. Use the ratio or the root test … 
PreCalculus
Q.Determine the sum of each infinite geometric series. t_1= 8 r = 2^1/2  A.This is a divergent series because the absolute value of r is greater than 1.  … 
Math
Does the following infinite geometric series diverge or converge?