AM PUS 40 DE PUNCTE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

1
+ 1 + 1 +......+ 1 =
1×2 2×3 3×4 2010×2011

1 + 1 + 1 +...+ 1 =
2  2^{2}  2^{3}  2^{2011}

1 + 1 + 1 +...+ 1 =
1+2 1+2+3 1+2+3+4 1+2+3+...2011

2

Răspunsuri

2014-07-09T11:57:34+03:00
 \frac{1}{1} *  \frac{1}{2} +  \frac{1}{2} *  \frac{1}{3} +   \frac{1}{3} *  \frac{1}{4} +...+ +

 \frac{1}{2010} *  \frac{1}{2011} =

se aduna 2 cate 2 => rezultatul este 1*2011=2011 deoarece sunt 2011 termeni

Cel mai inteligent răspuns!
2014-07-09T12:04:56+03:00

    1 /1x2+1 / 2 x3 +1 / 3x4 +......+1 /2010x2011=

    =1 / 1 -1 /2+1 /2-1 /3 +..........+1 /2010-1/2011(Se anuleaza si ramane):

   =1 /1- 1/2011=2010 /2011

     1 /1+2 + 1 /1+2+3 + 1/1+2+3+4 +..................+1/1+2+3+.....+2011=

   =1/2 x 3 /2 +1/3 x 4 /2 +...............+1/2011x2012 /2=

   =1: 2 x 3 /2+ 1:3 x 4 /2+.......+1: 2011 x 2012 /2=

   =1 x 2 /2 x 3 + 1 x 2 /3 x 4 +......+1 x 2 / 2011x2012=

    =2(1 / 2 x 3 + 2 /3 x 4 +...............+1 / 2011 x 2012)=

   =2(1 /2 - 1 /3 +1 /3 - 1 / 4+..................+1 / 2011 - 1 /2012)

   = 2(1 / 2 - 1 / 2012)=2 x 1005 /2012=2010 / 2012

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