Question

Calculati:
A=(1+2+3+...+50)-(1+2+3+...+30);
B=(1+2+3...+100)-(50+51+52+...+100)

Answer 1

Probabil ca stii formula 1+2+3+4+...+n=n(n+1)/2
Putem calcula A, B folosind doar aceasta formula:
B=(1+2+3+...49+50+51+...+100)-(50+51+52+...+100)=
1+2+3+....+49+(50-50)+(51-51)+.....+(100-100)=
1+2+3+...+49=49*50/2=49*25=1225

A=(1+2+3+...+50)-(1+2+3+...+30)=
(1-1)+(2-2)+...+(30-30)+31+32+33+...+50=31+32+33+...+50=
30+1+30+2+30+3+...+30+20=30*20+1+2+3+..+20=600+20*21/2=600+210=
810