# Calculus III

posted by .

Which of the following series are geometric series? Find the sum if they are

1.
Infinity (Summation sign) n = 1
1/6n^2

2.
Infinity (Summation sign) n = 1
(0.6)^n-1

• Calculus III -

1. Apparently you mean the sum from n=1 to n=infinity of 1/(6n^2)
= 1/(6*1) + 1/(6*4) + 1/6*9)
= (1/6)(1 + 1/4 + 1/9 + 1/16 + ...)]
This is not a geometric series. The ratio of successive terms is not a constant.

2. 0.6 + 0.6^2 + 0.6^3 + ...
= 0.6(1 + 0.6 + 0.6^2 + ...]
= 0.6/[1 - 0.6)= 1.5
This is a geometric series.

## Similar Questions

1. ### Calculus - ratio test

infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n->infinity) | [(e^n+1)/((n+1)!)] / [(e^n)/(n!)] | = lim (n->infinity) | [(e^n+1)/((n+1)!)] * [(n!)/(e^n)] | = lim (n->infinity) | ((e^n)(e^1)(n!)) …
2. ### calculus - ratio test

Posted by COFFEE on Sunday, July 29, 2007 at 6:32pm. infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n->infinity) | [(e^n+1)/((n+1)!)] / [(e^n)/(n!)] | = lim (n->infinity) | [(e^n+1)/((n+1)!)] …
3. ### calculus - ratio test

infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n->infinity) | [(e^n+1)/((n+1)!)] / [(e^n)/(n!)] | = lim (n->infinity) | [(e^n+1)/((n+1)!)] * [(n!)/(e^n)] | = lim (n->infinity) | ((e^n)(e^1)(n!)) …
4. ### Algebra

How do I write the terms of the series and find the sum. 4 summation notaion sign (k+6)^2 where k=1 under the summation sign
5. ### CALC 2

In the following series x is a real number. In each case, use the ratio test to determine the radius of convergence of the series. Analyze the behavior at the endpoints in order to determine the interval of convergence. a. Summation …
6. ### CALC 2 pls help!!

In the following series x is a real number. In each case, use the ratio test to determine the radius of convergence of the series. Analyze the behavior at the endpoints in order to determine the interval of convergence. a. Summation …
7. ### Calculus 2

In the following series x is a real number. In each case, use the ratio test to determine the radius of convergence of the series. Analyze the behavior at the endpoints in order to determine the interval of convergence. a. Summation …
8. ### Calculus 2

Determine whether the p-series is convergent or divergent. On top of the summation sign (∑) is infinity. Under the summation sign is n=1, and right next to it (to the right of ∑ sign) is 3/n^e. I was wondering how would …
9. ### Calculus 2

Use the Comparison Test to determine whether the series is convergent or divergent. On top of the summation sign (∑) is infinity. Under the summation sign is n=1, and right next to it (to the right of ∑ sign) is cos^2n/n^2. …
10. ### Calculus 2

Determine whether the series is convergent, absolutely convergent, conditionally convergent, or divergent. On top of the summation sign (∑) is infinity. Under the summation sign is n=2, and right next to it (to the right of ∑ …

More Similar Questions