J's answer to Noob student's Junior College 2 H2 Maths Singapore question.
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How I would present it: (yours is generally fine by the way)
1/xʳ = x⁻ʳ = x⁻² (x⁻⁽ʳ⁻²⁾)
Coefficient of 1/xʳ = coefficient of x⁻⁽ʳ⁻²⁾ in the brackets expansion
= (-2)(-3)(-4)...(-2 - (r - 2) + 1)/(r - 2)!
= (-2)(-3)(-4)...(1 - r)/(r - 2)!
= (2)(3)(4)...(r - 2)(r - 1)(-1)ʳ⁻² / (r - 2)!
= (r - 1)!(-1)ʳ(-1)² / (r - 2)!
= (r - 1)(-1)ʳ
1/xʳ = x⁻ʳ = x⁻² (x⁻⁽ʳ⁻²⁾)
Coefficient of 1/xʳ = coefficient of x⁻⁽ʳ⁻²⁾ in the brackets expansion
= (-2)(-3)(-4)...(-2 - (r - 2) + 1)/(r - 2)!
= (-2)(-3)(-4)...(1 - r)/(r - 2)!
= (2)(3)(4)...(r - 2)(r - 1)(-1)ʳ⁻² / (r - 2)!
= (r - 1)!(-1)ʳ(-1)² / (r - 2)!
= (r - 1)(-1)ʳ
Date Posted:
2 years ago
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