Question

va rog am nevoie de ajutor e urgent!!! (ex 34)​

Answer 1

Răspuns:

Explicație pas cu pas:

1 + 2 + 3 + ...+ 2010 = 2010*(2010 + 1)/2 = 2010*2011/2 = 1005*2011

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2010 - 2009 + 2008 - 2007 + ...+ 4 - 3 + 2 - 1

sunr 2010 termeni; rezultatul la fiecare grupa de doi termeni este 1 (2010 - 2009 = 1; 2008 - 2007 = 1; ....; 4 - 3 = 1; 2 - 1 = 1)

2010 - 2009 + 2008 - 2007 + ...+ 4 - 3 + 2 - 1 = 1*(2010 : 2) = 1005

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1/1*2 = 1 - 1/2

1/2*3 = 1/2 - 1/3

.......

1/2010*2011 = 1/2010 - 1/2011

1/1*2 + 1/2*3 +...+ 1/2010*2011 = 1 - 1/2 + 1/2 - 1/3 + ...+ 1/2010 - 1/2011

= 1 - 1/2011 = 2011/2011 - 1/2011 = 2010/2011

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1005*2011/1005 = x / (2010/2011)

2011 = x*2011/2010

x = 2011*2010/2011 = 2010