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iogann1982 [59]
2 years ago
13

Show that a sequence {sn} coverages to a limit L if and only if the sequence {sn-L} coverages to zero.

Mathematics
1 answer:
Andreyy892 years ago
3 0

Let {s_n}_{n\in\Bbb N} be a sequence that converges to L. This means for any \varepsilon>0, there is some N such that |s_n-L| for all n>N. From this inequality we see that |(s_n-L)-0|, so it follows that s_n-L\to0.

On the other hand, let {s_n-L} be a sequence that converges to 0. This means |(s_n-L)-0| for all large enough n, and we get the simpler inequality for free, |s_n-L|, so it follows that s_n\to L.

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Suppose that the second term of a geometric sequence is 4 and the sixth term is 16. Find the fourth term
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Answer:

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Step-by-step explanation:

<h3>Given GP</h3>
  • a₂ = 4,
  • a₆ = 16
<h3>To find</h3>
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<h3>Solution</h3>
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  • a₆= ar⁵ = 16

<u>Substitute ar in the second equation</u>

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  • 4r⁴ = 16
  • r⁴ = 4
  • r = √2

<u>Then finding a₄</u>

  • a₄ = a₂*r² = 4*(√2)² = 4*2= 8
7 0
2 years ago
Figure f is a scaled copy of Figure e.
Mekhanik [1.2K]

The correct equation of the scaled figure is given by 6/3 = 4/a

<h3>Scaling</h3>

Scaling is the process of either increasing or decreasing the size of a figure by a factor.

From the diagram attached, Figure f is a scaled copy of Figure e. Figure e is decreased to produce figure f, hence:

  • AB/XY = CD / WZ
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The correct equation of the scaled figure is given by 6/3 = 4/a

Find out more on scaling at: brainly.com/question/10253650

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8[12x - 24] + 6 = -2
Paladinen [302]

Answer:

x=2.75

Step-by-step explanation:

The answer will be correct.

7 0
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A

Step-by-step explanation:

A is false because irrational numbers can not be integers.

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Step-by-step explanation:

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