Find the sum. 1-2+3-4+5-6+7-8...99-100
1 answer:
Answer:
-50
Step-by-step explanation:
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8...99 - 100
just means,
1 - 2 = -1
3 - 4 = -1
5 - 6 = - 1
7 - 8 = - 1
99 - 100 = -1
basically, -1 + -1 + -1 + -1 + ....+ -1 or -1 - 1 - 1 - 1 - ... - 1
Treating Grandi's series as a divergent geometric series we may use the same algebraic methods that evaluate convergent geometric series to obtain a third value:
S = 1 − 1 − 1 + ..., so
1 − S = 1 − (1 − 1 − 1 ...) = 1 − 1 − 1 ... = S
1 - S = S
1 = 2*S
resulting in S = 1/2. The same conclusion results from calculating −S, subtracting the result from S, and solving 2S = 1
1/2 of the last term is 100 x 1/2 = 50
This because you are using 2 numbers per -1
example: 1 - 2 = -1 or 3 - 4 = -1 resulting in 50 of the -1 being subtracted
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See the explanation
<h2>Explanation:</h2>
A system that has one or infinitely many solutions is called <em>consistent. </em>If an equation in a system tells us no new information then the equations of the system are <em>dependent. </em>In other words, to find an equation that creates a consistent and dependent system with the given equation we have to get the same line:
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Graph of lines: brainly.com/question/14434483#
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Answer:
If there are 3 cats in the room, what is the ratio of ears to paws? 1 : 2
If there are 4 cats in the room, what is the ratio of paws to ears? 2 : 1
If all 5 cats are in the room, how many more paws are there than ears? the number of paws is twice as more than the number of ears, we have 10 more paws than ears.
Step-by-step explanation:
You can see the double number line for this situation in the attached photo.
So as we can see in the double number line diagram, if there are 3 cats in the room we would have an ears to paws ratio of 6 : 12 , which simplified would be 1 : 2, meaning that for every ear there are 2 paws.
For the next question, if there are 4 cats in the room, the paws to ears ratio would be 16 : 8, simplified to 2 : 1, meaning that for every 2 paws there is 1 ear.
And for the last question, if all 5 cats are in the room, we have that the paws to ears ratio is 20 : 10, simplified again to 2 : 1, meaning the number of paws is twice as more than the number of ears, so in this case we have 10 more paws than ears.
