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Is the sequence $2;-4;8;-16;...$ converging or not?
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Not converging

Explanation:

Given the sequence $2;-4;8;-16;..$, we can establish that the value of $r$, the common ratio is:

$r=\dfrac{T_{n+1}}{T_n} = \dfrac{T_2}{T_1}=\dfrac{-4}{2}=-2$

Using the formula for the general term of a geometric sequence:

$T_n=ar^{n-1}$

gives us

$T_n=2(-2)^{n-1}$

which does not converge because $r<1$.

by Wooden (4,853 points)

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