6. Let k > 0 be a constant and consider the important sequence {kn}. It's behaviour as n ® ¥ will depend on the value of k.
(i) State the behaviour of the sequence as n ® ¥ when k = 1 and when k = 0.
(ii) Prove that if k > 1 then kn ® ¥ as n ® ¥
(hint: let k = 1 + t where t > 0 and use th

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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 geometricseries. Hence show that:
S= 2sin x - 2^n+1 sin ((n+1)x) + 2^n+2 sin nx /

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Thanks for your expertise.
Part A Find a specific geometric that sums up to 30.
Part B Can you find a specific geometricseries that sums to -30 ?
Part C Can you find a specific geometricseries summing up to - ?
Part D Determine precisely which real numbers can be sums of

Please show how you arrived at the following solution
Use the geometric sequence of numbers 1, 2, 4, 8,..... to find the following :
a. What is r, the ratio between 2 consecutive terms
b. Using the formula for the nth term of a geometric sequence, what is the 24th term.

Use the geometric sequence of numbers 1, 3, 9, 27, ... to find the following:
a) What is r, the ratio between 2 consecutive terms?
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
c) Using the formula for the sum of a geometricseries, what is the sum of the first 10 terms?

Using the index of a series as the domain and the value of the series as the range, is a series a function?
Include the following in the answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, ration

N interfering waves of the same amplitude E_0 have relative phase-shift α with respect to one another (that is, the first wave is E_0, the second wave E_0 e^(iα), and so on, up to E_0 e^i(N-1)α). Find the amplitude and phase of the resulting disturbance.

Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8, ......to find the following:
a. What is r, the ratio between 2 consecutive terms?
b. Using the formula for the sum of the first n terms of a geometricseries. What is the sum of the first 10 terms? Please round your answer to 4 decimals.
c. Using the formula f