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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 function f(x) = 1.50x – 30 gives the amount of money Amelia has to spend each week for x school lunches, after taking money
Naya [18.7K]
To find the inverse, switch the x and y, and then solve for y (f(x) is the same as y)

So we get:
x=1.50y-30 (add 30 to both sides)
x+30=1.50y (divide both sides by 1.5)
x/1.5+30/1.5=y
y=x/1.5+20

Hope this helps
7 0
3 years ago
Solving the whole thing
erik [133]
Let
x---------------> distance from people living to the city center

we Know that
Zone 1 covers people living within three miles of the city center
Zone 1 ------------> [x < 3 miles]

Zone 2 covers those between three and seven miles from the center
Zone 2 ------------> [ 3 <= x < = 7  miles]

Zone 3 covers those over seven miles from the center
Zone 3 ------------> [  x > 7  miles]

<span>calculate the distance between two points to find the value of x
</span>
case A) point (0,0)  point (3,4)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(4-0)² +(3-0)²]------> √[16+9]
x=√25-------------> x=5 miles

the answer Part A)
people living in (3,4)
x=5 miles -------------> covers Zone 2 [ 3 < =x <= 7  miles]


case B) point (0,0)  point (6,5)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(5-0)² +(6-0)²]------> √[25+36]
x=√61-------------> x=7.81 miles

the answer Part B)
people living in (6,5) 
x=7.81 miles -------------> covers Zone 3 [  x > 7  miles]

case C) point (0,0)  point (1,2)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(2-0)² +(1-0)²]------> √[4+1]
x=√5-------------> x=2.23 miles

the answer Part C)
people living in (1,2) 
x=2.23 miles -------------> covers Zone 1 [ x < 3  miles]

case D) point (0,0)  point (0,3)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(3-0)² +(0-0)²]------> √[9]
x=√9-------------> x=3 miles

the answer Part D)
people living in (0,3) 
x=3 miles -------------> covers Zone 2 [ 3 < =x <= 7  miles]

case E) point (0,0)  point (1,6)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(6-0)² +(1-0)²]------> √[36+1]
x=√37-------------> x=6.08 miles

the answer Part E)
people living in (1,6) 
x=6.08 miles -------------> covers Zone 2 [ 3 < = x <= 7  miles]

4 0
3 years ago
2x+7 =5 is an example of...
tresset_1 [31]

Answer:

This is an example of distribution

Step-by-step explanation:

The reason why is because the equation is linear and if you exclud the y it show that it can distribute.

6 0
3 years ago
A bag of trail mix weighs 2 pounds. By weight, 18% is oats. Write a percent proportion to find weight of oats in mix
inysia [295]
2 pounds  ---- 100%
x pounds -----18%
x=(2*18)/100=36/100=0.36 pounds
8 0
3 years ago
Read 2 more answers
A plane flies with a speed of 600 mph. What distance will it fly
Vera_Pavlovna [14]

Answer:

3/5=360 mph 11/12=550 4/15=160

Step-by-step explanation:

4 0
3 years ago
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