Francis006
New Member
- Joined
- Jan 18, 2024
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- HSC
- 2024
The equation x^2+x+1=0 has roots a and b. Also, a series is defined by Tn=a^n+b^n for n=1,2,3,4...
a) Show that T1=-1 and T2= -1 (completed, but included for context)
b) Show that Tn = -Tn-1 - Tn-2 for n=3,4,5... (I have no clue from here)
c) Hence use induction to show that Tn=2cos(2nπ/3) for n=1,2,3...
d) Hence write down the value of Σn=2012 k=1 Tk
a) Show that T1=-1 and T2= -1 (completed, but included for context)
b) Show that Tn = -Tn-1 - Tn-2 for n=3,4,5... (I have no clue from here)
c) Hence use induction to show that Tn=2cos(2nπ/3) for n=1,2,3...
d) Hence write down the value of Σn=2012 k=1 Tk