Question

Problema 2, vă rog !

Answer 1

n=50k;   n∈N*

A={1;2;3;…….;n}

Suma elementelor mulțimii A:

1+2+3+……+n=n(n+1)/2=50k(50k+1)/2=25k(50k+1)

suma multiplilor lui 50=

=50•1+50•2+…..+50k

=50(1+2+…+k)=50•k•(k+1)/2=25k(k+1)

=> 25k(50k+1)- 25k(k+1)

=25k(50k+1-k-1)

=25k•49k

=(5•7•k)²

=(35k)²  este patrat perfect