Question

calculati radical A - 2009B unde
A= 2+4+6+...+4016 si B=2008* (1-1/2)(1-1/3)(1-1/4)...(1-1/2009)

Answer 1

Răspuns

Explicație pas cu pas:

Answer 2

$\it A=2+4+6+\ ...\ +4016=2(1+2+3+\ ...\ +2008)=2\cdot\dfrac{2008\cdot2009}{2}=\\ \\ \\ =2008\cdot2009\\ \\ \\ 2009B=2009\cdot2008\cdot\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)\cdot\ ...\ \cdot \left(1-\dfrac{1}{2009}\right)=\\ \\ \\ = 2009\cdot2008\cdot\dfrac{1}{\not2}\cdot\dfrac{\not2}{\not3}\cdot\dfrac{\not3}{\not4}\cdot\ ...\ \cdot\dfrac{\not2008}{2009}=2009\cdot2008\cdot\dfrac{1}{2009}=2008$

$\it\sqrt{A-2009B}=\sqrt{2008\cdot2009-2008}=\sqrt{2008(2009-1)}=\sqrt{2008\cdot2008}=\\ \\ =\sqrt{2008^2}=2008$