Lots of math questions for math club

  • Thread starter sabanation12
  • Start date
In summary: This can be expressed as 1/30 = 1/5 * 1/6, where 1/5 is the common denominator for all the fractions in the series. Therefore, the sum of the fractions would be 5/30 = 1/6. In summary, the conversation discussed various math problems including finding the sum of a series of fractions, determining the number at which two people counting at different rates will say at the same time, and finding the area of a shaded region between two concentric circles. The expert summarizer provided a solution for the first problem and suggested using a telescoping series for the second problem. They also clarified the use of "n" in the series and confirmed that the next number in
  • #1
sabanation12
21
0
We were given a worksheet just to see how much we knew and sucked at it, so now I am putting some time into trying to learn this stuff. Can you guys please answer these and tell me how you got them? and there is one i would love if you guys could check :)

First Question:

"Find the Sum of the following fractions"

1/2 + 1/6 + 1/12 + 1/20 + ... + 1/9900

"Express your answer as a common fraction"

Problem Two (is there a quick way you guys do this one?)

Julie begins counting backwards from 1000 by 2's and at the same time Tony begins counting foreward by 3's, if they count at the same rate what number will they say at the same time?

Problem 3 (check my work)

"A chord of the larger of two concentric circles is tangent to the smaller circle and measure 18 inches. Find the number of square inches in the area of the shaded region (area between outer rim of the inside circle and outer rim of the larger one). Express your answer in terms of ∏.

I did: 9^2 + r^2 = R^2 (r is radius of smaller circle R is radius of larger) and so then i simplified a little to get 81 = R^2 - r^2. Then ∏R^2 - ∏r^2 = ∏(R^2-r^2) and finally got ∏(81) as my final answer.
 
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  • #2
1/2+1/6+1/12+1/20+.....+1/9900
note that the numbers 2,6,12,20,...,9900 are of the form n(n+1)
so, nth term Tn = 1/n(n+1)
= 1/n - 1/(n+1)
so, the series is 1/1-1/2+1/2-1/3+1/3-1/4+....-1/99+1/99-1/100
= 1 - 1/100
= 99/100
 
  • #3
Question 2 :

1000 - (2x) = 3x
Solve for x
x = 200
Test it :
1000 - (2*200) = 600
3*200 = 600

So they say 600 at the same time.
 
  • #4
n(n+1)

Please elaborate, is "n" the denominator of the previous number?
 
  • #5
sabanation12 said:
n(n+1)

Please elaborate, is "n" the denominator of the previous number?

n=1 : 1(n+1) = 2
n=2 2(2+1) = 6
n=3 3(4) = 12
n=4 4(5) = 20
...
So n simply represents the set of number going 1 to 100.
Then we can reduce the series by using the same rule as a telescopic series to get the sum.

http://en.wikipedia.org/wiki/Telescoping_series
 
  • #6
So the next number in the series "1/2 + 1/6 + 1/12 + 1/20" would be 1/30? (5+1)*5
 
  • #7
Correct.
 

1. What types of math questions can we expect in a math club?

In a math club, you can expect a wide range of math questions covering various topics such as algebra, geometry, trigonometry, calculus, and more. The questions may range from basic concepts to more complex problem-solving tasks.

2. How can I prepare for math club meetings?

The best way to prepare for math club meetings is to practice solving different types of math problems. You can also review your notes from previous meetings and brush up on any topics that you may be struggling with.

3. Is it necessary to have a strong math background to participate in a math club?

No, it is not necessary to have a strong math background to participate in a math club. The purpose of a math club is to help students improve their math skills and learn new concepts. All levels of math proficiency are welcome in a math club.

4. How do math club meetings usually run?

Math club meetings can vary depending on the club, but they typically involve solving math problems individually or in groups, discussing solutions, and learning new concepts through interactive activities or presentations.

5. Can I join a math club at any time during the school year?

Yes, you can usually join a math club at any time during the school year. However, it is recommended to join at the beginning of the school year to get the most out of the club's activities and resources.

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