1. Mathematics
2. Geometry and Topology
3. Algebraic Geometry
4. 394817

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iv) Series C and S are defined as follows:
C=2cos x + 4 cos 2x + 8 cos 3x + ... + 2^n cos nx
S=2 sin x + 4 sin 2x + 8 sin 3x + ... + 2^n sin nx

Show that C+iS is a geometric series. Hence show that:

S= 2sin x - 2^n+1 sin ((n+1)x) + 2^n+2 sin nx / 5 - 4 cos x

Find a similar expression for C.