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ParthKohli
Group Title
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
 2 years ago
ParthKohli Group Title
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
 2 years ago

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

ParthKohli Group TitleBest ResponseYou've already chosen the best response.2
Am I correct?
 2 years ago

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

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

agentx5 Group TitleBest 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\(^n\) ? ) ;)
 2 years ago

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

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

agentx5 Group TitleBest 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
 2 years ago

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

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

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

agentx5 Group TitleBest ResponseYou've already chosen the best response.1
It starts at 1.
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.2
Oh, okay.
 2 years ago

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

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

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

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

ParthKohli Group TitleBest 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.
 2 years ago

agentx5 Group TitleBest 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?
 2 years ago

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

agentx5 Group TitleBest ResponseYou've already chosen the best response.1
dw:1342971841230:dw
 2 years ago

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

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

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

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

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

ParthKohli Group TitleBest ResponseYou've already chosen the best response.2
It does =)
 2 years ago

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

agentx5 Group TitleBest 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 ^_^
 2 years ago

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

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