Question

Calculati:
3+6+9+12+...+2001
5+10+15+...+2000
4+8+12+...+2000
7+14+21+...2002

Answer 1

3+6+9+12+...+2001 = 3·1 + 3·2 + .. + 3 · 667 = 3 ·(1 +2+ .. + 667 ) =
              = 3 · ( 1 +667 ) · 667 :2 = 3 · 668 · 667 :2 = 3 · 334  · 667
5+10+15+...+2000 = 5·1 + 5·2 + .. + 5· 400 =5· ( 1+2+ .. + 400 ) = 
             = 5 · ( 1 +400 ) · 400 :2 = 5 · 401 ·200
4+8+12+...+2000 = 4·1 + 4·2 + .. + 4·500  = 4· ( 1 +2+ .. + 500 ) 
 =4· ( 1 + 500 )· 500 :2 = 4· 501 · 250 = 1000 · 501
7+14+21+...2002 = 7 ·1 + 7· 2 + .. + 7·286  = 7· ( 1 +2+ .. + 286) = 
     = 7· ( 1 + 286 ) ·286 :2 = 7 · 287 ·143