Question

Cum se calculeaza, va rog:
1)S=2+4+6......+1024
2)S=3+6+9... ....+360
3)S=4+8+12......+440
4)S=5+10+15......5050
5)S=3+5+7.......101
6)S=2+7+12....507

Answer 1

1) S= 2(1+2+3+  + 512) = 2 x 512x513/2 = 512x513
2) S= 3(1+2+3+   + 120) = 3 x 120x121/2 = 180x121
3) S= 4(1+2+3+   +110) = 4 x 110x111/2 = 220x111
4) S= 5(1+2+3+   + 1010) = 5 x 1010x1011/2 = 2525x1011
5) S= 1+2 +3+2 + 5+2 +  +99+2 
1+3+5 +  + 99 = n^2
99= 2n+1 ==> n= 50 (50 termeni)
1+3+5+  +99 = 50^2 =2500
2x50 +2500 = 100+2500 = 2600
6) S=2+7+12 + +507= 2+2+5 +4+5 +  + 502+5 
2+4+  + 502 = 2( 1+2+  + 251) =2x 251x252/ 2 = 251x252
2+5x251 +251x252 = 2+1255 +251x252 = 1257 x 251x252