Sum of a Series Question  

  RSS

1

Find the sum of the first n terms of the following sequence.

(Not too hard, yet relatively nice to work out)

PlanckTime - Amin

 
0

I found nothing about this relatively nice. How did you do it? Mine looks horrible.

That one guy that's always on

How I did it was take Re(einx) = cos(nx), so that ∑3a - 1cos(ax) = Re(∑3a - 1eiax). This is then a geometric series with the inital value of eix and r = 3 eix. This gives Sn = Re(eix(1 - 3neinx)/(1 - 3eix)). This is a huge headache to spimlify and get an answer. Is there a better way to do this?

This is how I did it, and it isn't too bad to simplify if you multiply the denominator of your sum by  (1-3*exp(-ix))

That's what I did, but it left a nasty expression in the denominator.

0

Here's my solution, I don't think its too ugly!

PlanckTime - Amin

 
0

This is the best I could do:

That one guy that's always on

Yup, I agree with this

Share:
  
Working

Please Login or Register