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vampirchik [111]
3 years ago
15

Find the sum of the following infinite geometric series, if it exists. 2 + 6 + 18 + 54 +… Does not exist 23,567 25,982 29,034

Mathematics
1 answer:
Sladkaya [172]3 years ago
8 0

Option A: The sum for the infinite geometric series does not exist

Explanation:

The given series is 2+6+18+54+.......

We need to determine the sum for the infinite geometric series.

<u>Common ratio:</u>

The common difference for the given infinite series is given by

r=\frac{6}{2}=3

Thus, the common difference is r=3

<u>Sum of the infinite series:</u>

The sum of the infinite series can be determined using the formula,

S_{\infty}=\frac{a}{1-r}   where 0

Since, the value of r is 3 and the value of r does not lie in the limit 0

Hence, the sum for the given infinite geometric series does not exist.

Therefore, Option A is the correct answer.

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Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 4
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Answer:

  • \boxed{\sf Standard-form :x + 4y -17=0 }\\

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Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,

\longrightarrow x + 4y = 7\\

Firstly convert it into <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>i</em><em>n</em><em>t</em><em>e</em><em>r</em><em>c</em><em>e</em><em>p</em><em>t</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line which is <u>y</u><u> </u><u>=</u><u> </u><u>m</u><u>x</u><u> </u><u>+</u><u> </u><u>x</u><u> </u>, as ;

\longrightarrow 4y = -x + 7  \\

\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}\\

On comparing it to <em>y</em><em> </em><em>=</em><em> </em><em>m</em><em>x</em><em> </em><em>+</em><em> </em><em>c</em><em> </em>, we have ,

\longrightarrow m =\dfrac{-1}{4}\\

\longrightarrow c =\dfrac{7}{4}\\

Now as we know that the <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>o</em><em>f</em><em> </em><em>t</em><em>w</em><em>o</em><em> </em><em>p</em><em>a</em><em>r</em><em>a</em><em>l</em><em>l</em><em>e</em><em>l</em><em> </em><em>l</em><em>i</em><em>n</em><em>e</em><em>s</em><em> </em><em>i</em><em>s</em><em> </em><em>s</em><em>a</em><em>m</em><em>e</em><em> </em>. Therefore the slope of the parallel line will be ,

\longrightarrow m_{||)}=\dfrac{-1}{4}\\

Now we may use <em>p</em><em>o</em><em>i</em><em>n</em><em>t</em><em> </em><em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line as ,

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\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}} \\

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\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{  y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}\\

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