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sleet_krkn [62]
3 years ago
9

How do you prove that infinite sequences converge? For example how did someone prove that 1 + 1/4 + 1/9 + 1/16 + 1/25 ..... conv

erges to π^2/6. Can someone explain how people do this, and the process to discovering whether or not infinite sequences diverge or converge? An answer fully explaining the process, that is also fairly clear will receive a brainiliest.
Mathematics
1 answer:
dem82 [27]3 years ago
4 0

Answer:Prove that for any nonzero natural

n

it is true that

Sn=1+1/4+1/9+1/16+1/25+1/2<2

I'm sort of at a loss here. I'm not sure if there exists some formula or method to sum this kind of series, since there is a variable ratio…

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The table below shows the number of invertebrates found in a tide pool. Find the ratio of crabs to the total number of invertebr
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The ratio is 9:52. Meaning there is 9 crabs in the tide pool compared to all other invertebrates in the tide pool (including crabs). Crabs are also probably higher on the food chain because there is less of them, meaning they require more food then the other invertebrates.
Hope this helps!
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3 years ago
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alukav5142 [94]
The answer to that would be many
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3 years ago
Every attendant at a town's Chili Cook-off received a raffle ticket. There were 7 raffle prizes, including 5 that were food item
rjkz [21]

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0.2143

Step-by-step explanation:

4 0
3 years ago
Write an equation in slope-intercept form (y = mx + b).
Wewaii [24]

Answer:

y = 2/7x + 7

Step-by-step explanation:

We start off by putting the original equation into slope-intercept form. Subtract 7x from both sides, then divide both sides by -2. Your new equation should be y = -7/2x - 8. It's important to know that when two lines are perpendicular, their slopes (m) are opposite reciprocals of each other.  So -7/2 becomes 2/7. The first part of your final equation is y = 2/7x + b.

Next, we need to find the y intercept (b). You need to plug the x and y values from the given coordinate point (-7,5) into your final equation. You should end up with: 5 = 2/7(-7) + b. Then, solve for b.

5 = -14/7 + b

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7 = b

Finally, plug the b value into your final equation and you will have your answer.

4 0
3 years ago
I don't know how to do this
Dvinal [7]
a_1=2;\ r=-\dfrac{3}{2}\\\\a_2=a_1r\to a_2=2\cdot\left(-\dfrac{3}{2}\right)=-3\\\\a_3=a_2r\to a_3=-3\cdot\left(-\dfrac{3}{2}\right)=\dfrac{9}{2}\\\\a_4=a_3r\to a_4=\dfrac{9}{2}\cdot\left(-\dfrac{3}{2}\right)=-\dfrac{27}{4}\\\\a_5=a_4r\to a_5=-\dfrac{27}{4}\cdot\left(-\dfrac{3}{2}\right)=\dfrac{81}{8}
3 0
3 years ago
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