In statistics, what is the benefit of taking a sample survey rather than a census?

Taking a sample survey is quicker, cheaper and easier to carry out than a census. 

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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.


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Differentiate arcsin(2x) using the fact that 2x=sin(y)