Search over 10,000 free study notes

Need whiteboard throughout to properly answer, so will go through the ideas of what to do:

Take the base case of when n=1, and show that            (sum from 1 to 1) j = n(n+1)/2       is equal to ...

Simplify i⁴?

We know that i = -1^1/2

Therefore i²=-1

As i⁴=i²xi² 

Then i⁴=-1x-1=1

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