2 years ago

. Find the percent of change from 24 to 18.

Mathematics

1 answer:

oksano4ka [1.4K]2 years ago

8 0

Answer:

-25%

Step-by-step explanation:

18-24 = 24 x 100% = -25%

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Find the sum of the convergent series 7 0.7 0.007

mafiozo [28]

$7+0.7+0.007+\cdots=7\left(1+\dfrac1{10}+\dfrac1{100}+\cdots\right)$

Let $S_n$ denote the $n$ th partial sum of the series, i.e.

$S_n=1+\dfrac1{10}+\dfrac1{100}+\cdots+\dfrac1{100^n}$

Then

$\dfrac1{10}S_n=\dfrac1{10}+\dfrac1{100}+\dfrac1{1000}+\dfrac1{10^{n+1}}$

and subtracting from $S_n$ we get

$S_n-\dfrac1{10}S_n=\dfrac9{10}S_n=1-\dfrac1{10^{n+1}}$
$\implies S_n=\dfrac{10}9\left(1-\dfrac1{10^{n+1}}\right)$

As $n\to\infty$ , the exponential term vanishes, leaving us with

$\displaystyle\lim_{n\to\infty}S_n=\dfrac{10}9$

and so

$7+0.7+0.007+\cdots=7.777\ldots=\dfrac{70}9$