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Thanks soo much ..it was the 6k(k+1) that I was stuck on

Could some one help me with this mathematical induction question 2n^3-2n is divisible by 12 for integers n> and equal to 1

thanks but when you have cos(pi/2-nx/2)- isin(pi/2-nx/2)..why can you change it in the next line to cos (nx/2-pi/2) + isin (nx/2-pi/2) and the next line when you are subracting the denominator is that de moivre's rule . thanks again for your help

Thank you but what does the asterisk mean in line 3 and I don't understand line 3 where you have introduced the p what does the sin(pi/2-nx/2)-isin(pi/2-nx/2) come from...and then in the line that follows cos(nx/2-pi/2)+isin(nx/2-pi/2) come from\ THanks sorrry to be dumb

C = 1 + cos x + cos 2x +..... + cos (n-1)x S= sinx+sin2x+sin3x....+sin(n-1)x. i) Multiply series S by i ...... did this Ok ii) Write down C+iS ...did this Ok iii) If z=cosx+isinx, use de moivres to express c+is as a series in terms of z. .....did this Ok iv) Hence show that C + iS = (1-z^n)/...

i have a difficult complex no question can someone help out there please