Question

Calculați suma numerelor naturale de forma 2xy

Answer 1

xy-numar natural ,unde x,y∈N;
⇒xy∈[10,11,12,....,98,99];⇒90 de variante;
⇒2xy∈[210,211,212,......,298,299];
⇒210+211+212+....+298+299=[1+2+3+.....+299]-[1+2+3+....+209]
⇒[299·300/2]-[209·210/2]
⇒299·150-209·105=44850-21945=22905⇒suma numerelor;

Answer 2

Numerele de forma 2xy sunt:200,201,202........299
deci 299-200+1=100 de numere
200+201+...........299=(1+2+3+........+299)-(1+2+3+.....+199)
1+2+3+......+299=299x(299+1):2=299x300:2=89700:2=44850
1+2+3+......+199=199x(199+1):2=199x200:2=39800:2=19900
44850-19900=24950