Question

cum calculez exercitiul: 2+4+6+...2014

Answer 1

2 + 4 + 6 + ......... + 2 014 = 1 015 056

= 2 × ( 1 + 2 + 3 + ........ + 1 007 ) = → am dat factor comun pe 2

1 + 2 + 3 + .... + 1 007 = → aplic formula sumei lui Gauss

= 1 007 termeni × ( 1 + 1 007 ) / 2 =

= 1 007 x 1008 / 2 =

= 1007 × 504 =

= 507 528

________________

= 2 × 507 528 =

= 1 015 056

Answer 2

= 1+2+3+4+......+2014 :2 =

= 1+2+3+4+........+1007=

=> 1007 x 1008 :2 =

= > 1007 x 504 = 507528