Răspuns:
[tex]\color{DarkBlue}\boxed{ \boxed{\bf n = 35^{2} \longrightarrow patrat~perfect}}[/tex]
Explicație pas cu pas:
Cerința: Demonstrați ca n = 1 + 2 + 3+......+49 este pătrat perfect
[tex]\color{red}\boxed{\boxed{\bf Formula:S_{n}=1+2+3+4+....+n = \dfrac{n\cdot(n+1)}{2} }}[/tex]
[tex]\bf n =1+2+3+4+....+49 = \dfrac{49\cdot(49+1)}{2}[/tex]
[tex]\bf n =\dfrac{49\cdot50}{2}[/tex]
[tex]\bf n =49\cdot 25[/tex]
[tex]\bf n =7^{2} \cdot 5^{2}[/tex]
[tex]\bf n =(7\cdot 5)^{2} \implies[/tex]
[tex]\color{DarkBlue}\boxed{\boxed{\bf n = 35^{2} \longrightarrow patrat~perfect}}[/tex]
#copaceibrainly
