Tuesday

September 2, 2014

September 2, 2014

Posted by **Alanna** on Thursday, May 31, 2012 at 8:49pm.

- Math -
**MathMate**, Friday, June 1, 2012 at 12:15pmThe sum of the series ∑cos(nx) is, according to Mathworld,

N

∑cos(nx) = cos(Nx/2)sin((N+1)x/2) / sin(x/2)

n=0

(Note that the summation starts from 0, make adjustments accordingly).

The given series has x=1, or

S(1)=∑cos(n)

We see that the sum to N oscillates as N increases. Since we cannot find a value of N for whcih |T(n+1)|/|T(n)|<1 ∀n>N , we conclude that the series does not converge.

I make a difference between divergence where the sum approaches ±∞ and where the sum oscillates. I call the latter non-convergent.

**Answer this Question**

**Related Questions**

calculus - is this correct? use the integral test to determine if this series is...

Calculus - For what values of p>0 does the series Riemann Sum [n=1 to ...

Calc 2 - Is the series convergent or divergent? n=1 series to infinity (-1)^n...

calculus - Determine whether the series is convergent o divergent and say what ...

Calculus - Is the series 2/ln(n) convergent or divergent? n=3 to n=infinity

Calculus - ratio test - infinity of the summation n=1: (e^n)/(n!) [using the ...

Pre-calculus - Which of the following series is divergent? a) 1+3(1/4)+9(1/4)^2+...

Calculus - Determine whether the series is convergent or divergent. If it is ...

Calculus 2 - Find the radius of convergence and interval of convergence of the ...

calculus - ratio test - infinity of the summation n=1: (e^n)/(n!) [using the ...