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3 years ago

Determine whether the sequence converges or diverges. If it converges, give the limit. 108, -54, 27, -27/2

1 answer:

5 0

Hello,

a(1)=108
a(2)=a(1)/(-2)=-54
a(3)=a(2)/(-2)=a(1)/(-2)²=27
a(4)=a(3)/(-2)=a(1)/((-2)^3)=-27/2

a(n)=a(1)/(-2)^(n-1)=108 *(-1/2)^(n-1) (exponential decreasing)

lim if x->infinite (a(n))=0==> converges

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Step-by-step explanation:

Natalia divided a decimal number by an entire number. Since division is a operation derived from multiplication, the best approach to check if work was good is multiplying the given result by denomination, that is:

1) $x = 6.2\times 12$ Given.

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3) $x = 6\times 12 + 0.2\times 12$ Distributive property.

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7) $x = 72 + 24\cdot 10^{-1}$ Definition of multiplication.

8) $x = 72 + \frac{24}{10}$ Definition of divsion.

9) $x = 72 + 2.4$ Defintion of decimal number.

10) $x = 74.4$ Definition of addition/Result

Natalia's work is wrong.

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