Question

aratati ca nr a = 1+3+5+....+29 este patrat perfect

Answer 1

$a = 1+3+5+...+29 \\ a= (2\cdot \bold1-1)+(2\cdot \bold2-1)+(2\cdot \bold3-1)+...+(2\cdot \bold{15}-1) \\ \\\text{(avem 15 termeni)}\\ \\ a = 1+3+5+...+29\\a = 29+27+25+...+1\\ -------------(+)\\ \\ 2a = 30+30+30+\underset{de ~ 15 ~ ori}{\underbrace{...}}+30\\ \\ 2a=30\cdot 15\\ \\a = \dfrac{30\cdot 15}{2} \\ \\ a = 15\cdot 15 \\ \\ a = 15^2 \rightarrow\text{patrat perfect}$

Answer 2

(29-1):2+1=15 numere
a=(29+1)*15:2
a=30:2*15
a=15*15
a=15²=>a este patrat perfect

Sper ca te-am ajutat. Coroniță?