Question

Demonstrati ca numarul n+1+2+3+..+49 este patrat perfect
VA ROOG, URGEEEENTTTT​
va dau ce vreti voi, inima, 5 stele, coroana, doar ajutati maaaaa

Answer 1

Răspuns:

$\color{DarkBlue}\boxed{ \boxed{\bf n = 35^{2} \longrightarrow patrat~perfect}}$

Explicație pas cu pas:

Cerința: Demonstrați ca n = 1 + 2 + 3+......+49 este pătrat perfect

$\color{red}\boxed{\boxed{\bf Formula:S_{n}=1+2+3+4+....+n = \dfrac{n\cdot(n+1)}{2} }}$

$\bf n =1+2+3+4+....+49 = \dfrac{49\cdot(49+1)}{2}$

$\bf n =\dfrac{49\cdot50}{2}$

$\bf n =49\cdot 25$

$\bf n =7^{2} \cdot 5^{2}$

$\bf n =(7\cdot 5)^{2} \implies$

$\color{DarkBlue}\boxed{\boxed{\bf n = 35^{2} \longrightarrow patrat~perfect}}$

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