- #1
sony
- 102
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how to go from: [(1+n)^n]/n to: (1+1/n)^n ?
Can You Master the Equation (1+n)^n/n to (1+1/n)^n?
- Thread starter sony
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Homework Help Overview
The discussion revolves around the mathematical relationship between the expressions \((1+n)^n/n\) and \((1+1/n)^n\). Participants are exploring whether these two forms can be equated or transformed into one another.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Some participants question the validity of equating the two expressions, while others suggest examining limits and substitution of values as methods to explore the relationship. There is also a mention of basic algebraic principles related to fractions.
Discussion Status
The discussion includes various interpretations of the problem, with some participants expressing confusion and others providing insights into potential methods of exploration. There is no explicit consensus on the relationship between the two expressions, but the dialogue reflects an ongoing inquiry into the topic.
Contextual Notes
Participants note that checking by substituting values may not always yield valid conclusions, indicating a need for careful consideration of assumptions in the problem setup.
- #2
quasar987
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It's not true.
- #3
amcavoy
- 663
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Do you mean:
\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^{n}=\lim_{n\to 0}\left(1+n\right)^{\frac{1}{n}}.
\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^{n}=\lim_{n\to 0}\left(1+n\right)^{\frac{1}{n}}.
- #4
BerryBoy
- 176
- 1
http://www.berrys.plus.com/hh3.gif
You can check if you can get to a another equation by substuting values into 'n'.
Regards,
Sam
You can check if you can get to a another equation by substuting values into 'n'.
Regards,
Sam
Last edited by a moderator:
- #5
amcavoy
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Well, that doesn't always work (checking by substituting values). It's easy enough to show using algebra rules anyways.
- #6
BerryBoy
- 176
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Its true that it doesn't always work, but it is a quick method of proving something doesn't equate.
- #7
sony
- 102
- 0
Sorry, that's what I meant. Can you show me how you get to the right hand expression?BerryBoy said:
Last edited by a moderator:
- #8
matt grime
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you realize you're asking for someone to explain why (1+2)/2 = 1/2 +2/2, or more generally that (a+b)/c = (a/c)+(b/c), which is something you learn in primary/elementary school, right?
- #9
sony
- 102
- 0
matt grime said:
Oh, dear god... I can't believe I could be THAT silly
Of course I see it, my incredible dull brain was confused by the n's, probably.
Anyways, sorry for bothering you with this. That was rather embarrassing...
- #10
quasar987
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You just got grimed! Ouch.
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