Question

Efectuați 1 plus 2 minus 3 plus 4 plus 5 minus 6 plus 7 plus 8 minus 9 plus puncte puncte plus 2008 plus 2009- 2010 Plus 2011

Answer 1

Răspuns:

S = 674356

Explicație pas cu pas:

Se cere sa se calculeze suma :

S = 1+2-3+4+5-6+7+8-9+...............+2008+2009-2010+2011 = ?

___________________

Se observa ca numerele 3 , 6 , 9 ..... 2010

(din 3 in 3) sunt numere negative .

Transformam suma astfel :

S = 1+2+3+4+5+.....+2008+2009+2010+2011 - 2·(3+6+9....+2010)

S = S₁ - 2S₂

Calculam separat cele doua sume folosind suma lui Gauss:

S₁ = 1+2+3+...+2011 = (1+2011)·2011:2 = 1006·2011

S₂ = 3+6+9+....+2010 = (3+2010)·[(2010-3):3+1]:2

S₂ = 2013·670:2 = 2013·335  => 2S₂ = 2013·670

S = 1006·2011 - 2013·670 =  2023066 - 1348710

S = 674356