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Ileanacraiovean
a fost răspuns

(1- 1/2)(1-1/3)(1-1/4).....(1-1/2013).

va rog ajutati-ma si daca puteti sa explicati .

Răspuns :

Renatemambouko
(1- 1/2)(1-1/3)(1-1/4).....(1-1/2013)=
= 1/2×2/3×3/4×.....×2012/2013=
se observa ca se simplifica 2 cu 2, 3cu3, 4cu 4.....2012 cu 2012
=1/2013
[tex] \left( 1-\dfrac{1}{2}\right) \left( 1-\dfrac{1}{3}\right) \left( 1-\dfrac{1}{4}\right) \left( 1-\dfrac{1}{5}\right) ... \left( 1-\dfrac{1}{2012}\right) \left( 1-\dfrac{1}{2013}\right)= \\\;\\ \dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot \dfrac{4}{5}\cdot ... \cdot \dfrac{2011}{2012}\cdot\dfrac{2012}{2013}=\dfrac{1}{2013}[/tex]