Question

Efectuati:
10+20+30+...+2020-9-18-27-...-1818.

Answer 1

10 · ( 1 +2 +3 .. + 202 ) - 9 ·( 1 +2+ 3+ .. + 202)  = 
 = ( 10  - 9 ) · [ 1 +2 +3 +.. + 202] 
 =       1 · ( 1 + 202) ·202 /2 
  = 203 · 101 

Answer 2

$\displaystyle 10+20+30+...+2020-9-18-27-...-1818= \\ \\ =10(1+2+3+...+202)-9(1+2+3+...+202)= \\ \\ =10 \times \frac{202(202+1)}{2} -9 \times \frac{202(202+1)}{2} = \\ \\ = 10 \times \frac{202 \times 203}{2} -9 \times \frac{202 \times 203}{2} =10 \times \frac{41006}{2} -9 \times \frac{41006}{2} = \\ \\ =10 \times 20503-9 \times 20503=205030-184527=20503$