# Calculus - series

posted by .

Infinity of the summation n=0: [(-1)^n pi^(2n)] / [6^(2n) (2n)!]

this is my work:

[(-1^0) pi^(2*0)] / [6^(2*0) (2*0)!] + [(-1^1) pi^(2*1)] / [6^(2*1) (2*1)!] + [(-1^2) pi^(2*2)] / [6^(2*2) (2*2)!] + [(-1^3) pi^(2*3)] / [6^(2*3) (2*3)!]

-1 + -0.13707783 + -0.00313172 + -0.0000286 + -0.00000014

sum of the series = -1.14023829

You got the signs wrong. The answer is 1/2 sqrt[3]

thank you!!!

## 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. ### Calculus III

Which of the following series are geometric series?
5. ### Calculus

Does the series (1+sin(n))/(10^n) from summation 0 to positive infinity converge or diverge?
6. ### Calculus

Show that the following series is absolutely convergent: Summation from 1 to infinity: [(-1)^n * (n+1) * 3^n]/ [2^(2n+1)] I've done the ratio test and replaced n in this series with n+1. I get 3/4 in the end, which is less than 1, …
7. ### 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 …
8. ### 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 …
9. ### 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 …