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Plz advise why I maybe wrong?

Thanks

Asif

Problem Statement:

Use the formula for sum of a geometric progression to compute

exp(i[tex]\theta[/tex]) + exp(i2[tex]\theta[/tex]) +....+exp(in[tex]\theta[/tex])

and find formulas for trigonometric sums for

cos([tex]\theta[/tex]) + cos(2[tex]\theta[/tex])+....+cos(n[tex]\theta[/tex])

and

sin([tex]\theta[/tex]) + sin(2[tex]\theta[/tex])+....+sin(n[tex]\theta[/tex])

__Solution__A geometric progression sum: 1/1-r (assuming sequence is r, r^2,...r^n

Therefore for this problem, the sum will be

1/(1-exp(i[tex]\theta[/tex])) = 1/(1-cos [tex]\theta[/tex]) - isin([tex]\theta[/tex])

Taking conjugate of denominator above equation reduces to

1/2 + i sin([tex]\theta[/tex])/(2(1-cos([tex]\theta[/tex]))

Therefore

cos([tex]\theta[/tex]) + cos(2[tex]\theta[/tex])+....+cos(n[tex]\theta[/tex]) = 1/2

and

sin([tex]\theta[/tex]) + sin(2[tex]\theta[/tex])+....+sin(n[tex]\theta[/tex]) = sin([tex]\theta[/tex])/(2(1-cos([tex]\theta[/tex]))

__Problem:__1- Have I approached this problem in the right way

2- Does sum of cos = 1/2. Is this a property of cos? If so what is it called?