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oksano4ka [1.4K]
2 years ago
14

Im borxd wanna talk:)

Mathematics
1 answer:
Digiron [165]2 years ago
6 0

Answer:

ok

Step-by-step explanation:

Hi

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Find the number to which the sequence {(3n+1)/(2n-1)} converges and prove that your answer is correct using the epsilon-N defini
Nat2105 [25]
By inspection, it's clear that the sequence must converge to \dfrac32 because

\dfrac{3n+1}{2n-1}=\dfrac{3+\frac1n}{2-\frac1n}\approx\dfrac32

when n is arbitrarily large.

Now, for the limit as n\to\infty to be equal to \dfrac32 is to say that for any \varepsilon>0, there exists some N such that whenever n>N, it follows that

\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|

From this inequality, we get

\left|\dfrac{3n+1}{2n-1}-\dfrac32\right|=\left|\dfrac{(6n+2)-(6n-3)}{2(2n-1)}\right|=\dfrac52\dfrac1{|2n-1|}
\implies|2n-1|>\dfrac5{2\varepsilon}
\implies2n-1\dfrac5{2\varepsilon}
\implies n\dfrac12+\dfrac5{4\varepsilon}

As we're considering n\to\infty, we can omit the first inequality.

We can then see that choosing N=\left\lceil\dfrac12+\dfrac5{4\varepsilon}\right\rceil will guarantee the condition for the limit to exist. We take the ceiling (least integer larger than the given bound) just so that N\in\mathbb N.
6 0
3 years ago
How many of each color cubes are? .. answer please
ss7ja [257]

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2 cubes are red, 6 are blue, the rest are yellow so 8

Step-by-step explanation:

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yawa3891 [41]

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A, the probability is 1/9. you get this because you multiply the probabilities

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Step-by-step explanation:

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Step-by-step explanation:

\frac{1,5}{6} = 0,25 = \frac{25}{100} = 1:4

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