Question

2+4+6....+2010=;5+10+15.....+100=;3+6+9....+2007=;4+8+12......+148=;11+22+33+....+99=;7+14+21+.....+2009 dau coroana va rog

Answer 1

2+4+6+...+2010 = 2(1+2+3+...1005) = 2*1005*1006/2 = 1011030

3+6+9+...+2007 = 3(1+2+3+...+669) = 3*669*670/2 = 672345

4+8+12+...+148 = 4(1+2+3+...+37) = 4*37*38/2 = 2812

11+22+33+...+2009 = 11(1+2+3+...+9) = 11*9*10/2 = 495

7+14+21+...+2009 = 7(1+2+3+...+287) = 7*287*288/2 = 289286

(pentru calcularea sumelor din paranteze se foloseste formula lui Gauss)

Answer 2

2+4+6....+2010= 2·( 1 + 2 + 3 +.....+1005)= 2·[(1005·1006)]:2=1011030

paranteza este suma Gauss cu formula de calcul S =[n(n+1)]:2

unde n este ultimul termen al sumei

3 + 6 + 9 +...+ 2007 = 3·(1 + 2 + 3 +....+ 669) = 3·[669·670]:2 = 672345

4 + 8 + 12 +...+ 148 = 4·(1 + 2 + 3 +....+ 37) = 4·(37·38):2 = 2812

11 + 22 + 33 +...+ 2009 = 11·(1 + 2 + 3 +....+ 9) = 11·[(9·10)/2]= 495

7 + 14 + 21  +...+ 2009 = 7·(1 + 2 + 3 +....+ 287) = 7·[(287·288)]:2 = 289286