Question

sa se calculeze:
a)2+4+6+...+30-1-3-5-29
b)4+6+8+...+40-1-3-5-...-37

Answer 1

a )  2 + 4 + 6 + ..... + 30 - 1 - 3 - 5 - ..... - 29 = 15

= 2 × ( 1 + 2 + 3 + ...... + 15 ) - ( 1 + 3 + 5 + ..... + 29 ) = 15

= 2 × [ 15 × ( 1 + 15 ) :  2 } -  [ ( 29 - 1 ) : 2 + 1 } × 30 / 2 =

= 15 × 16 - 15 × 15 =

= 15 × ( 16 - 15 ) =

= 15

___________________________

b)   4 + 6 + 8 + ...... + 40 - 1 - 3 - 5 - ...... - 37 = 57

= 2 × ( 2 + 3 + 4 + ...... + 20 ) - ( 1 + 3 + 5 + ...... + 37 ) =

= 2 × 19 tremeni ×  ( 2 + 20 ) : 2  - [  ( 37 - 1 ) : 2 + 1 ] termeni × 38 / 2 =

= 19 × 22 - 19 × 19 =

= 19 × ( 22 - 19 ) =

= 19 × 3 =

= 57