Question

Calculați:3+5+7+...+2005-2-4-6-8-...-2004

Answer 1

Răspuns:

Explicație pas cu pas:

3 + 5 + 7 + .... + 2005 - 2 - 4 - 6 - 8 - ....... - 2004 = 1002

= ( 3 + 5 + 7 + ..... + 2005 ) - 2 × ( 1 +2 + 3 + ......+ 1002) =

→ (2005 - 3 ) : 2 + 1 = 1002 termeni are suma numerelor impare(5-3;..)

→ aplic formula sumei lui Gauss

= 1002 × ( 3 + 2005 ) : 2 - 2 × 1002 × (1 + 1002) : 2

=  1002 × 2008 : 2 -  1002 × 1003  =

= 1002 × 1004 - 1002 × 1003 =

= 1002 × ( 1004 - 1003) =

= 1002 × 1 =

= 1002

____________________________________________

Sau:

= ( 3 - 2 ) + ( 5 - 4 ) + ( 7 - 6 ) + ...... + ( 2005 - 2004 ) =

= 1 + 1 + 1 + 1 + ...... + 1 =

[______ de 1002 ori____]

= 1002

( 2005 - 3 ) : 2 + 1 = 1002 termeni are suma nr. impare

( 2004 - 2 ) : 2 + 1 = 1002 diferente