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The infinite series C and S are defined C = a*cos(x) + a^2*cos(2x) + a^3*cos(3x) + ..., and S = a*sin(x) + a^2*sin(2x) + a^3*sin(3x) + ... where a is a real number and |a| < 1. By considering C+iS, show that S = a*sin(x)/(1 - 2a*cos(x) + a^2), and find C.

C + iS = (a cos(x) + a^2 cos(2x) + a^3 cos(3x) + ...) + i( a sin(x) + a^2 sin(2x) + a^3 sin(3x) + ...) = a(cos(x) + i sin(x)) + a^2(cos(2x) + i sin(2x)) + a^3(cos(3x) + i*sin(3x)) + ... = a e^ix + a^2 e^i2x ...
SF
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An amount of money was invested for 8 years. It earned compound interest at 2.5% per year. After 8 years the total value of the investment was £11,696.67. Work out the total interest earned.

I would make sure the student new the difference between simple and compound interest to begin with. I would then explain the formula for compound interest and how it works normally. The formula is p(1+m)^n ...
LJ
Answered by Laura J. • Maths tutor
9913 Views

What is the mechanism for the nucleophilic substitution of a halogenoalkane?

A halogenoalkane is a saturated hydrocarbon chain with a halogen atom (F, Cl, Br or I) attached to a carbon instead of a hydrogen. Halogens have a greater electronegativity than carbon. This means they draw ...
CS
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How to factorise the expression x^2 + 8x + 15

We need to get the quadratic expression into the form (x + a)(x + b). If we expand this expression using FOIL, we see that the resulting expression is x 2 + (a+b)x + ab. We can now find a and b by comparing ...
CS
Answered by Charlotte S. • Maths tutor
4655 Views

How do you intergrate a function?

Increase the powers of all variables by one and then divide them by this number. For example, given 3x^3 + 5x^-0.5 - 8 , this would give 3/4x^4 + 10x^0.5 - 8x
DC
Answered by David C. • Maths tutor
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