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2 years ago

Answer 3. and 4. Please help me

Mathematics

1 answer:

AnnyKZ [126]2 years ago

4 0

ANSWER:

3. B) 21 times

4. C) 1 out of 2

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3 years ago

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Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.

Arisa [49]

Answer: $S_n=5(1-\dfrac{1}{n+1})$ ; 5

Step-by-step explanation:

Given series : $[\dfrac{5}{1\cdot2}]+[\dfrac{5}{2\cdot3}]+[\dfrac{5}{3\cdot4}]+....+[\dfrac{5}{n\cdot(n+1)}]$

Sum of series = $S_n=\sum^{\infty}_{1}\ [\dfrac{5}{n\cdot(n+1)}]=5[\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}]$

Consider $\dfrac{1}{n\cdot(n+1)}=\dfrac{n+1-n}{n(n+1)}$

$=\dfrac{1}{n}-\dfrac{1}{n+1}$

⇒ $S_n=5\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}=5\sum^{\infty}_{1}[\dfrac{1}{n}-\dfrac{1}{n+1}]$

Put values of n= 1,2,3,4,5,.....n

⇒ $S_n=5(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+......-\dfrac{1}{n}+\dfrac{1}{n}-\dfrac{1}{n+1})$

All terms get cancel but First and last terms left behind.

⇒ $S_n=5(1-\dfrac{1}{n+1})$

Formula for the nth partial sum of the series :

$S_n=5(1-\dfrac{1}{n+1})$

Also, $\lim_{n \to \infty} S_n = 5(1-\dfrac{1}{n+1})$

$=5(1-\dfrac{1}{\infty})\\\\=5(1-0)=5$

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3 years ago

how many more pairs of parallel sides does a regular octagon have than a regular octagon have than a regular hexagon

lana [24]

A regular hexagon has 3 pairs of parallel sides. A regular octagon has 4 pairs of parallel sides. Hope this helps :))

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3 years ago

Find the slope of the line that contains the points<br> (11, 8) and (17, 26)

amm1812

Answer:

Step-by-step explanation:

We can use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let's let (11,8) be x₁ and y₁ and let's let (17,26) be x₂ and y₂. So:

$m=\frac{26-8}{17-11}$

Subtract:

$m=18/6=3$

So, our slope is 3.

And we're done!

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3 years ago

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6+(w-10)=5 solve for w

andreyandreev [35.5K]

Answer:

w = 9

Step-by-step explanation:

9-10 = -1

6+-1 = 5.

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4 years ago