- #1

silvermane

Gold Member

- 117

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## Homework Statement

Find simple formulas for

1+ cos(θ) + cos(2θ) + cos(3θ) + ... + cos(nθ)

and

sin(θ) + sin(2θ) + sin(3θ) + ... + sin(nθ)

## The Attempt at a Solution

It's not really a homework question, but more for making a problem that I'm trying to solve a little bit more simple to calculate.

I know that

__1 + x + x^2 + ... + x^n = [x^(n+1) - 1]/[x-1]__

and I also know that

__u = cos(θ) +__

*i*sin(θ)I'm just having a little block in as how to incorporate these formulas to make my calculation a little easier.

You guys have always been great, and I do my best helping others with their combinatorics and linear algebra too. I know I'll get a wonderful answer, probably with some enrichment added on like icing to a cake. (just showing a little gratitude... I can't tell you how many times I've had wonderful educative experiences from this forum. It really does leave a positive mark on my life, lol)

Thank you in advance for your help! :) It means a lot to me!