2 years ago

In the box below, write the following statement using symbolic language.

Mathematics

1 answer:

ludmilkaskok [199]2 years ago

8 0

Answer: 1/3x-5=2x

This would be the same as the word problem because it is one third times x minus five equals two x.

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ra1l [238]

Answer:

The geometric series is where the ratio of consecutive terms is same.

We know that general representation of geometric series is:

$a,ar^2,ar^3....$

So, we say a given geometric series is :

Convergent if |r|<1 and converges at a/1-r

Diverges if |r|>=1

Example:

We have a series: 2,4,8,16

Here the common ratio of the above series is :

Formula for common ratio: $\frac{a_2}{a_1},\frac{a_3}{a_2}..$

Here, $r=\frac{4}{2}=2$

$r=\frac{8}{4}=2$

$r=\frac{16}{8}=2$

So, the common ratio is 2> 1 so, series diverges.

Now, we have a series

16,8,4,2...

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$r=\frac{4}{8}=\frac{1}{2}$

$r=\frac{2}{4}=\frac{1}{2}$

So, here r=1/2<1

Converging point is: a/1-r

Here, a=16, r=1/2 on substituting the values we get:

$\frac{16}{1-\frac{1}{2}}$

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