Question

2+4+6+...+18+20 suma lui gauss


11+22+33+...+110+121


111+222+333+...+999


5+10+15+...+845+850​

Answer 1

Explicație pas cu pas:

2× ( 1 + 2 + 3 +.... + 10) = (2× 10×11) / 2= 10×11 =

11 × ( 1 + 2 + 3 +...+ 10 + 11) = 11 × ( 11 × 12) / 2 =

111 × ( 1 + 2 + 3 +... + 9) = 111 × 9 ×10 /2 =

5× ( 1 + 2 + 3 +... + 169 + 170) = 5 × 170 × 171 / 2 =

Answer 2

Răspuns:

Explicație pas cu pas:

2+4+6+......+18+20 =

→ scriu fiecare termen al sumei ca produs de 2 factori, unul fiind 2

= 2×1+2×2+2×3+.....+2×9+2×10=

→ îl dau factor comun pe 2

= 2× (1+2+3+......+9+10) =

= 2 × 10 × ( 1+10) : 2 =

= 10 ×11 =

= 110

________________________

11+22+33+.....+110+121 =

=11×1+11×2+11×3 + ......+ 11×10 + 11×11 =

= 11 × ( 1+2+3+......+10+11) =

= 11 × 11 × (1+11) : 2 =

= 121 × 12 : 2 =

= 121 × 6 =

= 726

______________________

111 + 222 + 333 + ....... + 999 =

= 111 ×1 + 111×2 + 111×3 + ......+ 111×9 =

= 111 × ( 1+2+3+.....+9) =

= 111 × 9 × (1+9) : 2 =

= 999 × 10 : 2 =

= 9990 : 2 =

= 4995

___________________________________________________

5 + 10 + 15 + ....... + 845 + 850 =

= 5×1 + 5×2 + 5×3 + ........+ 5×169 + 5×170 =

= 5 × ( 1+2+3+......+ 169 + 170) =

= 5 × 170 × (1+170) : 2 =

= 850 × 171 : 2 =

= 145 350 : 2 =

= 72 675