- #1

- 92

- 0

from zero to infinity

a is a real number -1 < a < 1

I rewrote this as a geometric series involving a complex exponential

Real part of

[tex]\sum{(ae^{ix})^n}[/tex]

Which is a geometric series with common ratio r < 1, so it converges to the sum

(first term)/(1-r)

which seems to be

[tex]\frac{1}{1-ae^{ix}}[/tex]

taking the real part and multiplying top and bottom by (1-acosx), I get

[tex]\frac{1-acos(x)}{1-2acos(x) + a^2cos^2(x))}[/tex]

which is different from the desired result of

[tex]\frac{1-acos(x)}{1-2acos(x) + a^2)}[/tex]

Any help would be appreciated