Question

sa se arate ca numerele n=1997+2*(1+2+3+....+1995+1996) si p=1+3+5+...+1995+1997 sunt patrate perfecte.generalizare

Answer 1

1+2+3+...1996=1996*1997/2 =>n=1997+2*1996*1997/2=1997+1996*1997=1997(1+1996)=1997*1997=1997 La pătrat. P este o suma de nr omoare consecutive. Conform formulei sumei p=nr de termeni la pătrat. Nr de termeni =(1997-1)/2+1=1996/2+1=998+1=999 => p=999la patrat