Me ayudan con este ejercicio, se los agradecería muchourge¡?

S = [k(k + 1) / 2]

S = 2850

2S = k(k + 1)

2(2850) = k² + k

5700 = k² + k

k² + k - 5700 = 0 (Ecuacion de segundo grado)

Donde : a = 1 ; b = 1 ; c = - 5700

<img src="https://tex.z-dn.net/?f=k%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D" />

<img src="https://tex.z-dn.net/?f=k%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%5E2-4%281%29%28-5700%29%7D%7D%7B2%281%29%7D" />

<img src="https://tex.z-dn.net/?f=k%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%2B22800%7D%7D%7B2%7D" />

<img src="https://tex.z-dn.net/?f=k%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B22801%7D%7D%7B2%7D" />

<img src="https://tex.z-dn.net/?f=k%3D%5Cfrac%7B-1%5Cpm%20%5C%20151%7D%7B2%7D" />

k1 = [ - 1 + 151] / 2 = 150 / 2 = 75

k1 = 75

k2 = [ - 1 - 151] / 2 = - 152 / 2 = - 76

k2 = - 76

Tomo k1 = 75.

Probemos para k = 75

S = [(75(75 + 1)) / 2]

S = [(75x76) / 2]

S = [5700 / 2]

S = 2850

Rta : Se deben agregar 74 numeros mas apartir del 1.