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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.
 one year ago
 one year 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.
 one year ago
 one year ago

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

ParthKohliBest ResponseYou've already chosen the best response.2
@agentx5 I need a genius for this.
 one year ago

agentx5Best ResponseYou've already chosen the best response.1
Powers of two, while n is greater than or equal to 1. Yep! You're good
 one year ago

agentx5Best ResponseYou've already chosen the best response.1
Infinite sequence in fact, right? (i.e.: what's the limit as n goes to infinity for 2\(^n\) ? ) ;)
 one year ago

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

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

agentx5Best ResponseYou've already chosen the best response.1
This 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
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
dw:1342971644614:dw
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
But what if \(n\) is negative?
 one year ago

agentx5Best ResponseYou've already chosen the best response.1
n isn't negative. or zero
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
What if we have negatives included?
 one year ago

agentx5Best ResponseYou've already chosen the best response.1
\(\{n \} _{7 \ge n \ge 1}\) < this however has an upper boundary
 one year ago

agentx5Best ResponseYou've already chosen the best response.1
so... {2,4,8,16,32,64,128}
 one year ago

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

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

agentx5Best ResponseYou've already chosen the best response.1
Well for one thing you've got the wrong graph here, what happens when you raise to a negative power?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
Exactly, we have it getting closer to 0.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
Starts at 1 and keeps getting closer to 0.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
Oops. I posted the graph for \(x^2\).
 one year ago

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

agentx5Best ResponseYou've already chosen the best response.1
Yep sure does, as you approach negative infinity \[\huge \lim_{x \rightarrow \infty} 2^x = 2^{\infty} = (\frac{1}{2^{\infty}}) = \frac{1}{\infty} = 0\]
 one year ago

agentx5Best ResponseYou've already chosen the best response.1
See how the Algebra keeps coming back?
 one year ago

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

agentx5Best ResponseYou've already chosen the best response.1
I'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 ^_^
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
Heh. You're a nice guy!
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.2
And nice guys don't finish last ;)
 one year ago
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