Math Homework Woes: Extra Credit Assignment for My Son

In summary, the homework equation is S(n) = 1 + 1/2 + 1/3 + ... + 1/n. If n is greater than or equal to 66, then S(n) is greater than ln(n).
  • #1
Fatentity
3
0

Homework Statement


It's an extra credit assignment assigned by my math teacher, I sort of tried it but I'm not very good, and not too sure what else to do, this part isn't my strong suit.
Here's the problem:
(A)
"If my son would live forever and he grows 1 inch this week, 1/2 inch next week, 1/3 inch the week after that, ...etc. Then how old would my son be when he finally reaches 10 feet tall?
(Note: He's already 8 years old and 54 inches tall.)
(B) "If my son grows 1 inch this week, 1/4 inch next week, 1/9 inch the next week afte that, ...etc. Then what is the limit to how tall my son will grow (ie. What height will he get closer and closer to but never attain even if he lives forever?)

Homework Equations



http://en.wikipedia.org/wiki/Factorial

The Attempt at a Solution



I know it has to do with factorial (n!) and the n=1, 1/n and that side ways M thing *I forget the name*.

I tried...(Not sure how I can write that symbol)
Sn = /n!
1/n = 1+1/2+1/3+1/4...+1/n. 1 3 11 50
S(1) = 1
S(2) = 1 + 1/2 = 3/2 2x3x-3
S(3) = 1 + 1/2 + 1/3 = 11/6 4x3-1
S(4) = 1 + 1/2 + 1/3 + 1/9 = 35/18

So, I know the bottom is just n!, but I'm not sure about the top.

Besides that I'm not really too sure what to do. Help please! Thank you in Advance =].
Sorry I don't have much more work to show, just not too sure where to go.
 
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  • #2
Fatentity said:

Homework Statement


It's an extra credit assignment assigned by my math teacher, I sort of tried it but I'm not very good, and not too sure what else to do, this part isn't my strong suit.
Here's the problem:
(A)
"If my son would live forever and he grows 1 inch this week, 1/2 inch next week, 1/3 inch the week after that, ...etc. Then how old would my son be when he finally reaches 10 feet tall?
(Note: He's already 8 years old and 54 inches tall.)
(B) "If my son grows 1 inch this week, 1/4 inch next week, 1/9 inch the next week afte that, ...etc. Then what is the limit to how tall my son will grow (ie. What height will he get closer and closer to but never attain even if he lives forever?)

Homework Equations



http://en.wikipedia.org/wiki/Factorial

The Attempt at a Solution



I know it has to do with factorial (n!) and the n=1, 1/n and that side ways M thing *I forget the name*.
Sigma is the name of this Greek letter - [itex]\Sigma[/itex]
Fatentity said:
I tried...(Not sure how I can write that symbol)
Sn = /n!
1/n = 1+1/2+1/3+1/4...+1/n. 1 3 11 50
What's the purpose of 1, 3, 11, 50?
Fatentity said:
S(1) = 1
S(2) = 1 + 1/2 = 3/2 2x3x-3
S(3) = 1 + 1/2 + 1/3 = 11/6 4x3-1
S(4) = 1 + 1/2 + 1/3 + 1/9 = 35/18

So, I know the bottom is just n!, but I'm not sure about the top.
I think this is what you're trying to do. Here S(n) is the sum of the first n terms, 1 + 1/2 + 1/3 + ... + 1/n.
[tex]S(n)~=~\sum_{k = 1}^n \frac{1}{k}~=~1 + 1/2 + 1/3 + ... + 1/n[/tex]
The common denominator for the terms in the expanded summation is n!, but I'm not sure how you can use that fact.
Fatentity said:
Besides that I'm not really too sure what to do. Help please! Thank you in Advance =].
Sorry I don't have much more work to show, just not too sure where to go.
 
  • #3
It's going to be a long time. He has 66 more inches to go. Your sum:

Sn= 1 + 1/2 + ... + 1/n

doesn't have a nice simple closed form But it can be shown to be greater that ln(n). How large does n need to be for ln(n) > 66?
 

Related to Math Homework Woes: Extra Credit Assignment for My Son

1. Why do students struggle with math homework?

Many students struggle with math homework because it requires a combination of understanding concepts, memorizing formulas, and practicing problem-solving skills. Some students may also have a fear or negative attitude towards math, which can make the subject more difficult for them.

2. How can I help my child with their math homework?

One of the best ways to help your child with their math homework is to encourage them to practice regularly and ask for help when they need it. You can also offer support by reviewing their work and showing them alternative ways to solve problems.

3. Is extra credit necessary for my child's math homework?

Extra credit for math homework is not necessary, but it can provide an opportunity for students to challenge themselves and demonstrate their understanding of the material. It is ultimately up to the teacher to decide if extra credit will be offered.

4. What can I do if my child consistently struggles with math homework?

If your child consistently struggles with math homework, it may be beneficial to talk to their teacher and see if they can provide additional resources or support. You can also consider hiring a tutor who can work one-on-one with your child to address specific areas of difficulty.

5. How can I motivate my child to do their math homework?

Motivating your child to do their math homework can be challenging, but there are a few things you can try. You can offer incentives for completing homework, make math fun by incorporating games or real-life examples, or show your child the practical applications of math in everyday life.

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