Question

dany jest ciag geometryczny:3,-3,3,-3,3....wyznacz wzor ogolny tego ciagu.

oblicz a50.a51,S50,S51.

Answer 1

3, - 3, 3, - 3, ...

 

an = 3*( -1)^( n + 1)

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a50 = 3*( -1)^51 = 3*(-1) = - 3

a51 = 3*( -1)^52 = 3*1 = 3

oraz

S50 = 0

S51 = 3

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lub

a1 = 3

q = - 1

więc

S50 = 3*[ 1 - (-1)^50]/( 1 - (-1)) = 3*[ 1 - 1]/(1 + 1) = 0

S51 = 3*[ 1 - ( -1)^51]/( 1 - ( -1)) = 3*[ 1 + 1]/( 1 + 1) = 3

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