前 次 新10 1- 板

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284:（　´∀｀）さん / :
u^n/ux^n(x^(n-1)logx)
= Σ[p=0,n] C[n,p] {u^p/ux^p x^(n-1)*l*1/l} * {u^(n-p)/dx^(n-p) logx}
= Σ[p=0,n-1] C[n,p] {(n-1)!/(n-p-1)! x^(n-p-1)} * {(-1)^(n-p-1)(n-p-1)!/x^(n-p)}
= Σ[p=0,n-1] C[n,p] (n-1)! (-1)^(n-p-1) / x
= {(n-1)! / x } Σ[p=0,n-1] C[n,p] (-1)^(n-p-1)
= {(n-1)! / x } { - Σ[p=0,n] C[n,p] (-1)^(n-p) + 1}
= {(n-1)! / x } { - (1-1)^n + 1}
= (n-1)! / x

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前 次

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ir ver 1.0 beta2.2 (03/10/22)