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maksim [4K]
3 years ago
5

Determine whether the sequence converges or diverges. If it converges, give the limit.

Mathematics
1 answer:
ELEN [110]3 years ago
3 0

Answer:

The sequence converges to 0.

Step-by-step explanation:

Every new number is divided by 4 and will continue to grow smaller until it converges to 0.

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masha68 [24]
\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
% templates
f(x)=  A(  Bx+  C)+  D
\\\\
~~~~y=  A(  Bx+  C)+  D
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f(x)=  A\sqrt{  Bx+  C}+  D
\\\\
f(x)=  A(\mathbb{R})^{  Bx+  C}+  D
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f(x)=  A sin\left( B x+  C  \right)+  D
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--------------------

\bf \bullet \textit{ stretches or shrinks horizontally by  }   A\cdot   B\\\\
\bullet \textit{ flips it upside-down if }  A\textit{ is negative}\\
~~~~~~\textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }  B\textit{ is negative}

\bf ~~~~~~\textit{reflection over the y-axis}
\\\\
\bullet \textit{ horizontal shift by }\frac{  C}{  B}\\
~~~~~~if\ \frac{  C}{  B}\textit{ is negative, to the right}\\\\
~~~~~~if\ \frac{  C}{  B}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }  D\\
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~~~~~~if\   D\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{  B}

and with that template in mind.

3 units down, D = -3

4 units to the right, C = -4

f(x) = (x - 4)² - 3
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