2 + 4 + 6 + ...... + 42 = 462
= 2 × 1 + 2 × 2 + 2 × 3 + ..... + 2 × 21 =
= 2 × ( 1 + 2 + 3 + ....... + 21 ) =
= 2 × 21 × ( 1 + 21 ) : 2 =
= 21 × 22 =
= 462
__________________________
1 + 3 + 5 + 7 + ...... + 73 =
= 37 × ( 1 + 73 ) : 2 =
= 37 × 74 : 2
= 37 × 37 =
= 1 369
sau:
= 1 + ( 1 + 2 ) + ( 1 + 4 ) + ( 1 + 6 ) + ......... + ( 1 + 72 ) =
( 73 - 1 ) : 2 + 1 = 72 : 2 + 1 = 36 + 1 = 37 termeni are suma
= 1 × 37 + 2 × ( 1 + 2 + 3 + ........ + 36 ) =
= 37 + 2 × 36 × ( 1 + 36 ) : 2 =
= 37 + 36 × 37 =
= 37 × ( 1 + 36 ) =
= 37 × 37 =
= 1 369
_______________________
5 + 10 + 15 + .......+ 145 = 2 175
= 5 × 1 + 5 × 2 + 5 × 3 + ....... + 5 × 29 =
= 5 × ( 1 + 2 + 3 + ....... + 29 ) =
= 5 × 29 × ( 1 + 29 ) : 2 =
= 145 × 30 : 2 =
= 145 × 15 =
= 2 175
