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junior college 2 | H2 Maths
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@ J. Will this method be accepted
Date Posted: 2 years ago
Views: 564
Yes, in fact its the default/standard way.
Take note of presentation :
'Term in 1/x^r = ...' instead of ' 1/x^r = ... '
Also, r is a letter to symbolise the power of x in general so it doesn't = 2.
Take note of presentation :
'Term in 1/x^r = ...' instead of ' 1/x^r = ... '
Also, r is a letter to symbolise the power of x in general so it doesn't = 2.
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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
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