15. (a) Write down the sum of the geometric series z+ z² + z³ + · ·.+ z".(b) Hence, by putting z = e", show that:sin no sin (n + 1) 0sin 0sin 0 + sin 20 + sin 30 + .+ sin non-1)T(c) Deduce that sin + sin+ sin+ sin= cot .nnn2n

(a) The objective is to find the geometric series for z+z2+z3+...+zn. The formula for geometric…

15. (a) Write down the sum of the geometric series z + z? + z³ + · . .+ z". (b) Hence, by putting z = e, show that: i0 sin no sin (n + 1) 0 sin 0 sin 0 + sin 20 + sin 30 + + sin no ... –1)T п- (c) Deduce that sin + sin 2 + sin + sin = cot . 2n: ... n n n

15. (a) Write down the sum of the geometric series z + z? + z³ + · . .+ z". (b) Hence, by putting z = e, show that: i0 sin no sin (n + 1) 0 sin 0 sin 0 + sin 20 + sin 30 + + sin no ... –1)T п- (c) Deduce that sin + sin 2 + sin + sin = cot . 2n: ... n n n

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

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15. (a) Write down the sum of the geometric series z+ z² + z³ + · ·.+ z".
(b) Hence, by putting z = e", show that:
sin no sin (n + 1) 0
sin 0
sin 0 + sin 20 + sin 30 + .
+ sin no
n-1)T
(c) Deduce that sin + sin
+ sin
+ sin
= cot .
n
n
n
2n

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