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Chenkel's latest activity
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Chenkel
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Renato Iraldi's post
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Help understanding the Relativity of Simultaneity
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Informative
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To reason with time dilation we must take into account that in relativity you can only compare clocks that are in the same place, you...
Apr 18, 2024
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Chenkel
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PeroK's post
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I've been trying to understand the proof for the binomial theorem
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Like
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It's more compact that way. Note that the technique of splitting up the sum into two sums, re-indexing one (or both) of them, before...
Apr 3, 2024
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Chenkel
replied to the thread
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I've been trying to understand the proof for the binomial theorem
.
That helps a lot in me understanding, thank you!
Apr 3, 2024
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Chenkel
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PeroK's post
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I've been trying to understand the proof for the binomial theorem
with
Like
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PS the proof could be simplified somewhat by noting that it is sufficient to prove the identity when ##a = 1##. Then, as a corollary we...
Apr 3, 2024
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Chenkel
reacted to
PeroK's post
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I've been trying to understand the proof for the binomial theorem
with
Love
.
An alternative for the inductive proof is: $$(a + b)^{n+1} = (a+b)(a+b)^n = (a + b)\sum_{k = 0}^n \binom n k a^{n-k}b^k$$$$= \sum_{k =...
Apr 3, 2024
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Chenkel
posted the thread
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I've been trying to understand the proof for the binomial theorem
in
General Math
.
Hello everyone, I've been trying to understand the proof for the binomial theorem and have been using this inductive proof for...
Apr 2, 2024
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Chenkel
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PeroK's post
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Question about change of variables
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Yes. That's a valid scenario. In that case, the integral on the left-hand side will always be zero. You can look at the proof above...
Mar 14, 2024
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Chenkel
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Question about change of variables
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As I've pointed out several times(!), the proof uses the chain rule and goes in the opposite direction from the usual change of...
Mar 14, 2024
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Chenkel
replied to the thread
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Question about change of variables
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So ##\int_a^b f(u(x))u'(x)dx = \int_{u(a)}^{u(b)} f(t)dt## is still true when ##u(a) = u(b)##?
Mar 14, 2024
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Chenkel
replied to the thread
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Question about change of variables
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The fact that the proof you provided for the change of variables definite integration equation doesn't work with a non-injective ##u##...
Mar 14, 2024
C
Chenkel
replied to the thread
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Question about change of variables
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I agree that the left hand side of that equation doesn't equal the right side, and I think I see the general problem, if ##u=\sin...
Mar 14, 2024
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Chenkel
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PeroK's post
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Question about change of variables
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I'm a little surprised that you don't see the general problem. It's the null interval. Although, perhaps it wasn't the best example...
Mar 14, 2024
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Chenkel
replied to the thread
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Question about change of variables
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I'm not sure what you mean by somethings going wrong there. The integral ##\int_0^{2\pi} \sin \theta \ d\theta## is 0 using the...
Mar 14, 2024
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Chenkel
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PeroK's post
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Question about change of variables
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Yes. Here's how it can go wrong. With ##x = \sin \theta##, we have: $$\int_0^{2\pi} \sin \theta \ d\theta = \int_0^0 \dots$$And it's a...
Mar 13, 2024
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Chenkel
replied to the thread
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Question about change of variables
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Interesting, thank you for the insight!
Mar 13, 2024
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