Question

Fie suma de nr naturale consecutive S=8+9+10...+50.
a) Sa se arate ca S=1247.
b)Aflați n€ IN dacă Sn jos =8+9+10+...+50+51+...+n=1742

Answer 1

Răspuns

Suma Gauss:

a) 50*51:2-7*8:2=1275-28=1247

b) n(n+1):2-7*8:2=1742

n(n+1):2-28=1742

n(n+1):2=1742+28

n(n+1):2=1770

n(n+1)=3540

3540=59*60 =>

n=59