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 2 years ago
Notation of a sequence:
What do we mean by \(n \ge 1\) in \(\{ 2^n\}_{n \ge 1}\)?
Is it all the terms of the sequence only have \(n = 1\) or more? So basically \(n\) iterates to the positive numbers.
 2 years ago
Notation of a sequence: What do we mean by \(n \ge 1\) in \(\{ 2^n\}_{n \ge 1}\)? Is it all the terms of the sequence only have \(n = 1\) or more? So basically \(n\) iterates to the positive numbers.

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ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2So, the sequence is \(\{2,4,8,16\cdots \}\).

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2@agentx5 I need a genius for this.

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1Powers of two, while n is greater than or equal to 1. Yep! You're good

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1Infinite sequence in fact, right? (i.e.: what's the limit as n goes to infinity for 2\(^n\) ? ) ;)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2Ah! Great stuff! \(\{ 1,2,3,4,5,6,7\} = \{n \} _{7 \ge n \ge 1}\)

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2It never reaches anywhere, so it's infinity. That was an oral question :P

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1This is how you typically see these though, as series (sums of the terms in a sequence) \(\sum_{n \ge 1}^{\infty} 2^n\) = \(\infty\) or "Diverges" as they say

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1342971644614:dw

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2But what if \(n\) is negative?

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1n isn't negative. or zero

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2What if we have negatives included?

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1\(\{n \} _{7 \ge n \ge 1}\) < this however has an upper boundary

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1so... {2,4,8,16,32,64,128}

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2The limit is 0 if we have \(\{ 2^n\}_{n \le 0}\) right?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2I believe that the sequence \(\{2,4,8,16,32,64,128 \}\) doesn't have a limit.

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1Well for one thing you've got the wrong graph here, what happens when you raise to a negative power?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2Exactly, we have it getting closer to 0.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2Starts at 1 and keeps getting closer to 0.

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2Oops. I posted the graph for \(x^2\).

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2\[\lim _{x \to \infty} 2^x = 0\] Good enough?

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1Yep sure does, as you approach negative infinity \[\huge \lim_{x \rightarrow \infty} 2^x = 2^{\infty} = (\frac{1}{2^{\infty}}) = \frac{1}{\infty} = 0\]

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1See how the Algebra keeps coming back?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2I believe that I'd owe you a lot when I get into MIT :)

agentx5
 2 years ago
Best ResponseYou've already chosen the best response.1I'm used to tutoring students with learning disabilities :) That's my parttime job on campus. Maybe you can help me find a job at some point in the future, ya never know ^_^

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2Heh. You're a nice guy!

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.2And nice guys don't finish last ;)
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