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Pliss potrzebuje pomocy z tym zadaniem Oblicz sumę: -1 +5 -25 + ... +78125=.

Odpowiedź :

Odpowiedź:

Sn = a₁ * [tex]\frac{1-q^{n}}{1-q}[/tex]

aₙ = a₁ * [tex]q^{n-1}[/tex]

q = -5

78125 = -1 * [tex]-5^{n-1}[/tex]

-78125 = [tex]-5^{n-1}[/tex]

-78125 = [tex]-5^{7}[/tex]

[tex]-5^{n-1}[/tex] = [tex]-5^{7}[/tex] -----> n = 8

S₈ = -1 * [tex]\frac{1-(-5)^{8} }{1-(-5)} = -1 * \frac {1-390625}{6} = -1 * (-65104) = 65104[/tex]