Question

Fie numerele A=(1+1/2)×(1+1/3)×(1+1/4)×........×(1+1/2013);
B=(1-1/2)×(1-1/3)×(1-1/4)×......×(1-1/2012)
a) Determinați numerele A si B
b) Arătați ca A×B>0,5


P.S. / inseamna supra
DAU COROANA.

Answer 1

a) calculam fiecare paranteza
A=(3/2)*(4/3)*(5/4)*     .....*(2013/2012)*(2014/2013)
simplificam
A=2014/2=1007

pt B, la fel, calculam fiecare paranteza
B=(1/2)*(2/3)*(3/4)*............*(2010/2011).*(2011/2012)
 simplificam,
B=1/2012
 

b) A*B=(1007/2012)>(1006/2012)=1/2=0,5