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C + iS = (acos(x) + a^2cos(2x) + a^3cos(3x) + ...) + i( asin(x) + a^2sin(2x) + a^3sin(3x) + ...)
= a(cos(x) + isin(x)) + a^2(cos(2x) + isin(2x)) + a^3(cos(3x) + ...
For n = 1, the sum is given by (1/2)(1)(1+1), which gives 1, the expected result. We now assume that the statement is true for some k. If we look at k+1, the sum is given by 1 + 2 + ... + k + (k+1). Since...
xln(x) - x
Some of these examiners quite like asking students to find the derivative of an inverse trig or hyperbolic function to try and catch someone off guard. The best way to approach these is to first multiply ...
First we check that this is true for n=1: S1 = 1/(1x3) which is equal to n/(2n+1) for n=1 therefore Sn = n/(2n+1) is true for n = 1. Next assume that it is true for n=k. SkJFAnswered by Jamie F. • Further Mathematics tutor13101 Views
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