Răspuns :
1+2+3-4+5+6+7-8+...+97+98+99-100=
1+2+3+4-4-4+5+6+7+8-8-8...+97+98+99+100-100-100=
1+2+3+4+5+6+7+8+...+97+98+99+100-2x(4+8+12+...+100)=
(100x101):2-2x4(1+2+3+...+25)=
50x101-2x4x25x26:2=
5050-100x26=5050-2600=2450
am folosit formula de adunare a primelor n nr, naturale, adica:
1+2+3+...+(n-1)+n=nx(n+1):2
1+2+3+4-4-4+5+6+7+8-8-8...+97+98+99+100-100-100=
1+2+3+4+5+6+7+8+...+97+98+99+100-2x(4+8+12+...+100)=
(100x101):2-2x4(1+2+3+...+25)=
50x101-2x4x25x26:2=
5050-100x26=5050-2600=2450
am folosit formula de adunare a primelor n nr, naturale, adica:
1+2+3+...+(n-1)+n=nx(n+1):2