# Proving Equations through Homework

• prace
In summary, the two people are having trouble solving a homework problem. One person is trying to solve it using substitution and another is trying to solve it by using the infinite product.
prace

## Homework Statement

The question asked was to "Show that..." with regards to the equations stated below.

## Homework Equations

http://album6.snapandshare.com/3936/45466/862870.jpg

sorry for such a large image... I am not too savvy with the latex yet, so i just linked an image that i created with microsoft word.

## The Attempt at a Solution

So, I know I am suppossed to show an attempt at this solution, but I am completely boggled on where to even start. One thing I did try to do for the first equation was to just substitute in values for n starting at 2. This did not really do much for me because as I continued along, the equation just came out to be ln(1-(some number smaller and smaller than 1)).

The only thing I can take out of the second equation is that the series will converge at pi, but I don't see how that is going to help me. I also tried substitute in numbers for n but again, no help there. I did find out however that the series was an alternating series, but I guess that was pretty obvious from the original statement of the problem.

Any help with getting me started with this would be greatly appreciated!

Last edited by a moderator:
Hint $$\sum_k \ln a_k = \ln\prod_k a_k$$

The first series should probably start at 2, but it can not start at 1 because it it does than it is undefined.

benorin said:
Hint $$\sum_k \ln a_k = \ln\prod_k a_k$$

Hi,

Thanks for the responses. Sorry for the dumb question, but what does the symbol in the right hand side of the equation after the ln mean? I don't think I have seen that one before. thanks.

prace said:
Hi,

Thanks for the responses. Sorry for the dumb question, but what does the symbol in the right hand side of the equation after the ln mean? I don't think I have seen that one before. thanks.

It's an infinite product.

cool thanks, I am going to try and figure it out! I'll be back =)

## What is the purpose of proving equations through homework?

The purpose of proving equations through homework is to reinforce understanding of mathematical concepts and to develop problem-solving skills. By practicing and proving equations, students can solidify their understanding of mathematical principles and apply them to real-world situations.

## How can proving equations through homework help students learn?

Proving equations through homework allows students to actively engage with the material and apply it in a practical way. It also provides an opportunity for students to identify and correct any mistakes they may have made, promoting a deeper understanding of the concepts being taught.

## What strategies can be used to effectively prove equations through homework?

Some effective strategies for proving equations through homework include breaking down the problem into smaller, more manageable steps, using visual aids such as diagrams or graphs, and checking the solution for accuracy. It is also helpful to discuss and explain the steps and thought processes used to arrive at the solution.

## What are the benefits of proving equations through homework?

Proving equations through homework can improve critical thinking skills, increase problem-solving abilities, and enhance overall comprehension of mathematical concepts. It also allows students to practice and apply their knowledge, leading to a deeper understanding and retention of the material.

## How can teachers support students in proving equations through homework?

Teachers can support students in proving equations through homework by providing clear instructions and examples, offering guidance and feedback, and creating a supportive and collaborative learning environment. It is also important for teachers to address any misconceptions or difficulties students may have and provide additional resources for further practice if needed.

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