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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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Jonas runs a pet store that sells guinea pigs. He wants to ensure he has more than 1 pound of dry food for every foge guinea pig
Amiraneli [1.4K]
You can do this by converting this into a ratio or a fraction

Ratio:
1 lb for 4 guinea pigs
1:4
If he was 8 lbs for x guinea pigsit would be

1:4
8:x

Multiply the first ration until the one is equal to 8, then whatever the four turns into is x

Fraction: (easier way)

1/4 (1lb for 4 guinea pigs)
8/x (8lb for x guinea pigs)
1/4 = 8/x
Multiply one until it is equal to 8
Correspond that to the 4

1*8 = 8
4*8 = 32

32 guinea pigs

8 0
3 years ago
Read 2 more answers
What are the angle measurements of 6x + 1° = 3x + 11°
hodyreva [135]

Answer:

x=3\frac{1}{3}^\°

Step-by-step explanation:

Given equation:

6x+1\°=3x+11\°

To find the angle measure of x   

Solution:

In order to find the angle measure x , we will isolate x on left side by carrying out math operations on both sides.

We have:

6x+1\°=3x+11\°

Subtracting both sides by 3x  

6x-3x+1\°=3x-3x+11\°

 3x+1\°=11\°

Subtracting both sides by 1°.

3x+1\°-1\°=11\°-1\°

3x=10\°  

Dividing both sides by 3.

\frac{3x}{3}=\frac{10\°}{3}

x=\frac{10}3}^\°

Converting fraction to mixed number by dividing and writing the quotient as whole number and the remainder as numerator.

∴  x=3\frac{1}{3}^\°  (Answer)

7 0
3 years ago
Can someone help me asap??
Zepler [3.9K]
You need help on what ?
8 0
3 years ago
Read 2 more answers
A bullet train traveling at 275 kilometers per hour. At that rate, how many kilometers will the train travel in 2-1/2 hours
aleksklad [387]
To find the answer,we can simply multiply 275 by 2-1/2:

275×2-1/2

=275×(2×2+1)/2

=275×5/2

=1375/2

=678-1/2

Therefore, the answer is 678-1/2.

Hope it helps!
5 0
3 years ago
The Harper family is traveling to visit friends. The distance to the friend’s house is 276.45 miles. It takes the family 5.82 ho
yawa3891 [41]
The family travels 47.5 miles per hour.
7 0
3 years ago
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