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Is the sequence $2;-4;8;-16;...$ converging or not?
in Mathematics by Wooden (4,853 points)
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Answer:

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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