I managed the first parts, its the last part im having trouble with. (let x be theta)
This part was fine and the sum of the convergence series wasAn infinite series is given by z - z^2 + z^3 - z^4
i.) Assuming the series converges, find an expression for the sum.
ii.) Given that z = 1/4(cos x + isin x) explain why the series converges for all values of x.
So i assume we use this for part b.)
b.) By using de moivres theorm or otherwise, prove that the sum of the infinite series
Well im not sure how to do this by de moivres theorm...but by series:
Sum of infinite series:
So for a being the first in the series, this must be the imaginary part of
And r, the common ration must be imaginary part of
So the convergence is imaginary part of:
Which can be re-arranged to get:
Well the numerator is the same as required in the question however im not sure how to get the denominator...or in fact if i have even done this right.
Any help would be greatley appriciated