joi, octombrie 09, 2008

calcul sume...remember?

Pun aici repede, repede , o problema (rezolvata ...sa nu aiba nimeni emotii ;-) de clasa a VII, care mi-a dat de furca, atit mie cit si prietenilor mei , toti inteligenti si cu scoli destepte absolvite intr-un trecut mai mult sau mai putin indepartat.


Sa se compare sumele:

a=1-1/2+1/3-1/4+.......................+1/2004

b=1/1003+1/1004+.....................+1/2004

Rezolvare:

a = (1+1/3+1/5+.........+1/2003) – (1/2+1/4+1/6+................+1/2004)

a = (1+1/3+1/5+.........+1/2003) – 2 (1/2+1/4+1/6+................+1/2004) + (1/2+1/4+1/6+................+1/2004)

a =1+1/3+1/5+.........+1/2003 – 1 -1/2-1/3-1/4-1/5-...........-1/1002 + 1/2+1/4+1/6+................+1/2004

a = 1+1/3+1/5+.........+1/2003 – 1 -1/2-1/3-1/4-1/5-...........-1/1002 + 1/2+1/4+1/6+................+1/2004

Reducind termenii rezulta:

a=1/1003+1/1005+............+1/2003+1/1004+1/1006+..................+1/2004

a=1/1003+1/1004+1/1005+..............+1/2004

=> a=b

Sper sa-i foloseasca vreunui studios cindva, undeva...:-)

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