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.

Question

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.

parthkohli · Answer

So, the sequence is $\{2,4,8,16\cdots \}$.

parthkohli · Answer

Am I correct?

parthkohli · Answer

@agentx5 I need a genius for this.

anonymous · Answer

Powers of two, while n is greater than or equal to 1.  Yep!  You're good

anonymous · Answer

Infinite sequence in fact, right?  (i.e.:  what's the limit as n goes to infinity for 2$^n$ ? ) ;-)

parthkohli · Answer

Ah! Great stuff!
$\{ 1,2,3,4,5,6,7\} = \{n \} _{7 \ge n \ge 1}$

parthkohli · Answer

It never reaches anywhere, so it's infinity.
That was an oral question :P

anonymous · Answer

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

parthkohli · Answer

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