Question

47 Calculați:
a) (-2)²+(-2)² + (-2)³+...+(-2) 100 =
b) (-3)¹ +(-3)² + (-3)³ + ... + (-3) 75 =​

Answer 1

Orice numar negativ la o putere para este un numar pozitiv

Orice numar negativ la o putere impara este un numar negativ

a)

$(-2)^1+(-2)^2+...+(-2)^{100}=\\\\Notam\ S=(-2)^1+(-2)^2+...+(-2)^{100}\ \ \ |\cdot (-2)\\\\-2S=(-2)^2+(-2)^3+...+(-2)^{100}+(-2)^{101}\ \ \ |+(-2)\\\\-2S-2=(-2)^1+(-2)^2+(-2)^3+...+(-2)^{100}+(-2)^{101}\\\\-2S-2=S+(-2)^{101}\\\\3S=-2-(-2)^{101}\\\\S=\frac{2^{101}-2}{3}$

b)

$S=(-3)^1+(-3)^2+...+(-3)^{75}\ \ \ |\cdot (-3)\\\\-3S=(-3)^2+(-3)^3+...+(-3)^{75}+(-3)^{76}\ \ \ |+(-3)\\\\-3S-3=(-3)^1+(-3)^2+(-3)^3+...+(-3)^{75}+(-3)^{76}\\\\-3S-3=S+(-3)^{76}\\\\4S=-3-(-3)^{76}\\\\S=\frac{-3^{76}-3}{4}$

Un alt exercitiu gasesti aici: https://brainly.ro/tema/9445131

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