- #1
How is this equality possible? What did the professor do to reach it?
- Context: Undergrad
- Thread starter tahlaskerssen
- Start date
-
- Tags
- Professor
Click For Summary
Discussion Overview
The discussion revolves around understanding a mathematical equality presented by a professor, specifically how one term in an expression relates to another. Participants seek clarification on the manipulation of logarithmic terms and the concept of factoring sums in a mathematical context.
Discussion Character
- Exploratory, Technical explanation, Conceptual clarification
Main Points Raised
- Some participants express confusion about the transformation of terms in a mathematical expression, specifically how one term relates to another.
- One participant mentions a professor's reference to "factoring sums out," seeking clarification on this concept.
- A participant describes the expression as being of the form: A. ln Q - A. ln w, where A is a common factor in both terms, suggesting that the summations can be combined due to their common range.
- Another participant explains that the logarithmic terms can be combined using the identity ln Q - ln w = ln (Q/w) and notes that this can be simplified further to ln (Q/w) = - ln (w/Q).
- A participant reflects on their initial misunderstanding of combining series and expresses a desire to improve their understanding of the topic.
Areas of Agreement / Disagreement
Participants generally agree on the mathematical manipulation of the terms, but there is no consensus on the initial confusion regarding the concepts involved.
Contextual Notes
Some participants indicate a lack of familiarity with the concept of combining series and logarithmic identities, suggesting a potential gap in foundational knowledge that may affect their understanding.
- #2
NascentOxygen
Staff Emeritus
Science Advisor
Homework Helper
- 9,253
- 1,080
tahlaskerssen said:
Can someone explain me how one term got to the other term? It makes no sense to me
Your image is not publicly accessible. Can you change its permissons?
- #3
tahlaskerssen
- 10
- 0
NascentOxygen said:
I uploaded it.
By the way, he said something about "factoring sums out" what is that supposed to mean? This is the first time I've ever encountered something like this and i have taken up to differential equations regarding my math level.
- #4
NascentOxygen
Staff Emeritus
Science Advisor
Homework Helper
- 9,253
- 1,080
The expression is of the form: A. ln Q - A. ln w
where A is a long summation and common to both terms.
Besides A, ln Q is the other term inside the first summation (likewise, besides A, you can see that ln w is the other term in the second series).
As each summation is over the same range, then you can combine the two series in one, using just one sigma.
Then combine the terms into one making use of: ln Q - ln w = ln (Q/w)
finally remember: ln (Q/w) = - ln (w/Q)
It looks forbidding, but really isn't.
Basically, write the expression without the ∑ symbol, and simplify what you see.
EDITED
where A is a long summation and common to both terms.
Besides A, ln Q is the other term inside the first summation (likewise, besides A, you can see that ln w is the other term in the second series).
As each summation is over the same range, then you can combine the two series in one, using just one sigma.
Then combine the terms into one making use of: ln Q - ln w = ln (Q/w)
finally remember: ln (Q/w) = - ln (w/Q)
It looks forbidding, but really isn't.
Basically, write the expression without the ∑ symbol, and simplify what you see.
EDITED
Last edited:
- #5
tahlaskerssen
- 10
- 0
i'm so stupid.. i deserve to go start college again.. Thanks a lot man!(honestly, i didnt know you could combine two same series into one, i was just treating them as a normal number and they were cancelling each other or getting a sigma squared, lol)
Similar threads
- · Replies 25 ·
- · Replies 4 ·
- · Replies 58 ·
- · Replies 7 ·
- · Replies 4 ·
- · Replies 4 ·
Undergrad
De-dimensionalizing/rescaling units
- · Replies 6 ·
- · Replies 14 ·