![antoniocapetillo80](/avatars/25769.jpg)
antoniocapetillo80
29.03.2021 •
Mathematics
Pls tell me the perimeter of this question
Solved
Show answers
More tips
- C Cities and Countries Which Country has the Most Expensive Visa?...
- F Family and Home Tender Care for Your Parquet: Is it Possible to Clean Parquet?...
- S Society and Politics Is It Fact or Fiction? Let s Talk About Anton Chekhov s Pseudonym...
- S Sport Playing Bowling: Rules and Advice for Novices...
- C Computers and Internet How to Properly Repartition a Hard Drive?...
- A Auto and Moto What Is the Cost of Customs Clearance for a Car in Russia?...
- L Leisure and Entertainment Should You Buy a Ceramic Knife?...
- C Computers and Internet How to easily and quickly disable Firebug in Gmail and Google Docs...
- G Goods and services How to sew a ribbon: Tips for beginners...
- F Food and Cooking How to Make Mayonnaise at Home? Secrets of Homemade Mayonnaise...
Answers on questions: Mathematics
- M Mathematics What is the correct order...
- M Mathematics there are 641 boys and 490 girls in greenland school. Each child makes 8 art pieces for classroom decorations. All the art pieces are then distributed eqaully among 58 classrooms....
- M Mathematics How many solutions are in 10(x + 4) – 3 = 14x + 1...
- M Mathematics A scuba diver descends farther down into the ocean from an initial depth of 14.7 feet below sea level. The scuba diver descends at a constant rate for 412 minutes and reaches...
- M Mathematics Keeping special cause variation from occurring is the essence of statistical quality control. a. True b. False...
- M Mathematics What is the greatest common factor of the terms in the polynomial 4x^4 – 32x^3 – 60x^2? A 4 B 4x C 4x^2 D 4x^3...
- M Mathematics Help im stuck today is my birthday Find a15 for the sequence: -1, 4, -16, 64, ... Question 4 options: 1,073,741,824 -268,435,456 -67,108,864 -1024...
- M Mathematics What’s the answer for 135.826 - 57.12...
- M Mathematics A grasshopper jumps at a 65.0° angle at 5.42 m/s. At what time does it reach its maximum height? (Unit = S)...
- M Mathematics What is the answers for these...
Ответ:
Ответ:
You will never reach a sum of 2. You would need infinitely many terms to sum up.
Explanation:
We have this sequence
1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ...
which is geometric with the following properties
a = first term = 1r = common ratio = 1/2 = 0.5Notice how we multiply each term by 1/2 to get the next term. Eg: (1/4)*(1/2) = 1/8 or (1/16)*(1/2) = 1/32.
Since r = 0.5 is between -1 and 1, i.e. -1 < r < 1 is true, this means that adding infinite terms of this form will get us to approach some finite sum which we'll call S. This is because the new terms added on get smaller and smaller.
That infinite sum is
S = a/(1-r)
S = 1/(1-0.5)
S = 1/0.5
S = 2
So if we keep going with that pattern 1+1/2+1/4+... and do so forever, then we'll reach a sum of 2. However, we cannot go on forever since it's asking when we'll reach that specific sum. In other words, your teacher wants finitely many terms to be added.
In short, we'll never actually reach the sum 2 itself. We'll just get closer and closer.
Here's a list of partial sums
1+1/2 = 1.51+1/2+1/4 = 1.751+1/2+1/4+1/8 = 1.8751+1/2+1/4+1/8+1/16 = 1.93751+1/2+1/4+1/8+1/16+1/32 = 1.968751+1/2+1/4+1/8+1/16+1/32+1/64 = 1.9843751+1/2+1/4+1/8+1/16+1/32+1/64+1/128 = 1.99218751+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 = 1.99609375We can see that we're getting closer to 2, but we'll never actually get there. We'd need to add infinitely many terms to get to exactly 2.