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Pentru E(x) = [tex]\frac{x+1}{x-1}[/tex] calculati E(-2)·E(-3)·E(-4)·...·E(-100)

Răspuns :

Răspuns

5050

Explicație pas cu pas:

[tex]E(-2)\cdot E(-3)\cdot E(-4)\cdot\ldots\cdot E(-100)=\\\\=\dfrac{-2-1}{-2+1}\cdot\dfrac{-3-1}{-3+1}\cdot\dfrac{-4-1}{-4+1}\cdot\ldots\cdot\dfrac{-99-1}{-99+1}\cdot\dfrac{-100-1}{-100+1}=\\\\\\=\dfrac{-3}{-1}\cdot\dfrac{-4}{-2}\cdot\dfrac{-5}{-3}\cdot\dfrac{-6}{-4}\cdot\ldots\cdot\dfrac{-98}{-96}\cdot\dfrac{-99}{-97}\cdot\dfrac{-100}{-98}\cdot\dfrac{-101}{-99}=\\\\\\=\dfrac{1}{-1}\cdot\dfrac{1}{-2}\cdot(-100)\cdot(-101)=\dfrac{100\cdot 101}2=50\cdot 101=5050. [/tex]

Green eyes.