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seen Apr 24 '13 at 10:58

Undergraduate theoretical physics student.

Interests:

Physics: all areas of fundamental physics.

Math: all areas related to the above.

(specifically, the interface of theoretical physics and mathematics)


Sep
30
asked General question on relation between infinite series and complex numbers
Sep
30
revised Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
added 515 characters in body
Sep
29
comment Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
[Plus, as per FredrikMeyer's comment ["You want to show that $r^n \rightarrow 0$ as $n \rightarrow \infty$ provided |r|<1. So let ϵ > 0 be given. Then $r^n \lt ϵ$ is equivalent to n ≥ ln ϵ/ ln r. Such an n exists."] I'm not sure why you would claim a "formal" $\epsilon$-$\delta$ proof of the statement would not be applicable.]
Sep
29
comment Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
@Arturo: The issue of the epsilon-delta proof comes from the following: [comment # 5] "first I derive the formula for the finite series as $S_n = a\frac{(r^n−1)}{r−1}$; then, I claim that, if |r| < 1, convergence of the series is equivalent to claiming that: $\lim_{n \rightarrow \infty} |S_{n+1}−S_n| = \lim_{n \rightarrow \infty} |ar^n| = 0$. But I'm wondering how to prove this." ... I'm wondering if this is a valid approach to the initial problem [the first part of]?
Sep
29
comment Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
Srivatsan, +1. Thanks. Appreciate greatly.
Sep
29
comment Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
@Arturo: Can you provide your perspective on how best to prove the above [in question body]? I think my general approach is in the right direction, but maybe you can suggest a better method / methods. -cheers
Sep
29
awarded  Peer Pressure
Sep
29
revised Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
added 241 characters in body; edited title
Sep
29
comment Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
@Fredrik: I've never done a formal $\epsilon - \delta$ proof before. Can you provide a detailed version for a complete newbie to fully understand. ... (Would appreciate greatly.) :)
Sep
29
comment Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
@wnoise: by using the derived formula (partial sum formula) I then claim that if |r| < 1, the expression tends to a limiting values (i.e. 'sum' S) as successive differences tend to zero as n tends to infinity. I need to prove that successive differences (|$S_{n+1} - S_n$|) tend to zero (for n $\rightarrow \infty$). .. I'm currently trying to find the exact epsilon-delta argument to demonstrate this.
Sep
29
comment Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
@wnoise: I need to demonstrate that the series converges; if it does, the sum has meaning. I can't use the concept of sum if I cannot first demonstrate that the series converges.
Sep
29
comment Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
@Fredrik: Can you provide a full epsilon-delta proof for this? This is where I'm stuck [for first part].
Sep
29
comment Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
@J.M.: I need a sort of epsilon-delta proof if I'm not mistaken.
Sep
29
comment Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
[Derivation for $S_n = a \frac{(r^n-1)}{r-1}$ was by simple algebraic manipulation. I don't need any assistance with that.] ... The specific issue I have with first part of first proof is, how to prove above claim.
Sep
29
comment Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
Basically, first I derive the formula for the finite series as $S_n = a \frac{(r^n -1)}{r-1}$; then, I claim that, if |r| < 1, convergence of the series is equivalent to claiming that: lim$_{n \rightarrow \infty}$ |$S_{n+1} - S_n$| = lim$_{n \rightarrow \infty}$ |$ar^n$| $\rightarrow$ 0. But I'm wondering how to prove this. ...
Sep
29
asked Show that the geometric series $a + ar +ar^2 + \cdots + ar^{n-1} + \cdots$ converges if and only if $|r| < 1$
Sep
17
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
Ok. Thanks. - regards
Sep
17
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
Ref: math.stackexchange.com/questions/tagged/education ... Plus, the description field is empty. ...
Sep
17
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
I've looked through the posts with that tag. I found mostly questions similar to mine. ... I think the posts with that tag are different for the two sites. ... (Need clarification here.)
Sep
17
revised Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
edited tags