/sci/ - Science & Math » Thread #11157492

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Anonymous Mon 18 Nov 14:16:00 2019 No.11157492 View Reply Original Report

Quoted By: >>11157514 >>11157521 >>11157527

How do I calculate this limit?

Anonymous

Anonymous Mon 18 Nov 2019 14:27:28 No.11157514 Report

Quoted By:

>>11157492
Thanks god I don't have CRT screen, turning it around would be really heavy lifting to read your post.

~S/$\S~

~S/$\S~ Mon 18 Nov 2019 14:30:14 No.11157521 Report

Quoted By:

>>11157492
How do you limit a calculator?

Anonymous

Anonymous Mon 18 Nov 2019 14:32:44 No.11157527 Report

Quoted By: >>11157546 >>11157551 >>11157853 >>11158125

>>11157492
x^m - 1 = (x-1)(x^(m-1) + .. + x + 1)
x^n - 1 = (x-1)(x^(n-1) + .. + x + 1)
x^m - 1/x^m - 1 = (x^(m-1) + .. + x + 1)/(x^(n-1) + .. + x + 1)
Set x = 1, (x^(m-1) + .. + x + 1)/(x^(n-1) + .. + x + 1) = m/n.
So the limit is m/n

~S/$\S~

~S/$\S~ Mon 18 Nov 2019 14:44:08 No.11157546 Report

Quoted By:

>>11157527
AMAZING

IF I DIVINE THE DIVISION, I AVOID DERISION.

THANK YOU BASED OP!

~S/$\S~

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~S/$\S~ Mon 18 Nov 2019 14:46:52 No.11157551 Report

Quoted By: >>11157552

>>11157527
Also, just if you're curious...

Anonymous

Anonymous Mon 18 Nov 2019 14:47:36 No.11157552 Report

Quoted By: >>11157556

>>11157551
what is this?

~S/$\S~

~S/$\S~ Mon 18 Nov 2019 14:49:36 No.11157556 Report

Quoted By:

>>11157552
A complex-argument hyper-geometric proof of OP's query to satisfy separation of geometric identities from factorials and non-differentiable exponents.

Anonymous

Anonymous Mon 18 Nov 2019 17:55:17 No.11157853 Report

Quoted By: >>11158157

>>11157527
or just use l'Hospital.

Anonymous

Anonymous Mon 18 Nov 2019 19:48:02 No.11158118 Report

Quoted By: >>11158125

x^m-1 = (1+h)^m-1 +o(h) = m*h+o(h)
x^n-1 = n*h+o(h)

divide the two:
m/n

Anonymous

Anonymous Mon 18 Nov 2019 19:49:23 No.11158125 Report

Quoted By:

>>11158118
and the advantage of this is that it works for any real-valued exponents, while >>11157527 works only for natural numbers

Anonymous

Anonymous Mon 18 Nov 2019 20:06:53 No.11158157 Report

Quoted By:

>>11157853
This

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