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 ) =

= 2 × 15 × 16 / 2 - [ ( 29 - 1 ) : 2 + 1 ) × ( 1 + 29 ) / 2 ] =

= 15 × 16 - ( 15 × 30 / 2 ) =

= 240 - 225 =

= 15

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

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

= 2 × [ ( 20 - 2 + 1 ) × ( 2 + 20 ) ] / 2 -  [ ( 37 - 1 ) : 2 + 1 ) × ( 1 + 37 ) / 2 ] =

= 19 × 22 - 19 × 38 / 2 =

= 19 × ( 22 - 19 ) =

= 19 × 3 =

= 57