Cⁿ₁ is always positive, then the second term has negative sign.
What is meant by binomial expansion?
The theorem that specifies the expansion of any power (a + b)m of a binomial (a + b) as a certain sum of products aibj, such as (a + b)2 = a2 + 2ab + b2.
The i-th term of the binomial expansion [tex](x- y)^{n}[/tex]
Ti = nCi - 1 . (x)ⁿ+¹⁺i . (-y)i - 1
For any n, when i=2,
T₂ = nC₂₋₁ . xⁿ⁺¹⁻² . (-y)²⁻¹ = -Cⁿ₁ xⁿ⁻¹ . y
Since is always positive, then the second term has negative sign.
Cⁿ₁ is always positive, then the second term has negative sign.
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