Question

Clasa a 5 a,suma lui Gauss 1+3+5+...+21-2-4-6...-20=

Answer 1

1 + 3 + 5 + ...... + 21 - 2 - 4 - 6 - ....... - 20 = 11

= ( 1 + 3 + 5 + ...... + 21 ) - ( 2 - 4 - 6 - ..... - 20 ) =

= [ 1 + ( 1 + 2 ) + ( 1 + 4) + ..... + ( 1 + 20 ) ] - 2 × ( 1 + 2 + 3 + ...... + 10 ) =

= [ ( 1 + 1 + .... + 1 ) + 2 × ( 1 + 2 + 3 + .... + 10 ) ] - 2 × 10 × ( 1 + 10 ) : 2 =

= [ 1 × 11 + 2 × 10 × ( 1 + 10 ) : 2 ] - 10 × 11 =

= ( 11 + 10 × 11 ) - 110 =

= 121 - 110 =

= 11