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Things that are equal to 1 
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#19
Feb2613, 11:00 AM

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P: 1,391




#20
Feb2613, 11:04 AM

P: 531

Hmm, I guess I don't understand Gamma...
The results of (1/2)! and (1/2)! are different as you indicate. Gamma takes precedence in the order of operations? I'll take a look at Gamma. 


#21
Feb2613, 11:49 AM

HW Helper
P: 1,391

It can be shown that for x = n, where n is an integer, ##\Gamma(n+1) = n!##. The trick with the noninteger factorials comes from abusing this notation in the case where x is not an integer, i.e., writing ##\Gamma(x+1) = x!##. From this it may be easier to see why (x)! is different from (x!). Edit: to keep this post somewhat on the actual topic, one of the forms of 1 that I use often enough is introducing ##1 = z^\ast/z^\ast## when I want to rewrite a complex number ##1/z## in a more convenient form with the imaginary and real parts readily obvious: $$\frac{1}{z} = \frac{1}{z}\times 1 = \frac{1}{z} \frac{z^\ast}{z^\ast} = \frac{z^\ast}{z^2}.$$ 


#23
Feb2713, 03:32 PM

Mentor
P: 11,589

$$0.\bar{9}$$
$$\lim_{n \to \infty} \sqrt[n]{n}$$ More general, for every real a: $$\lim_{n \to \infty} \sqrt[n]{n^a} 


#24
Feb2713, 04:39 PM

P: 7

e^(i*pi*2k) where k is an integer



#26
Feb2713, 04:44 PM

P: 7

Pretty sure its a more general euler's equation



#28
Feb2713, 11:13 PM

P: 13

Ʃ(1/2^k) from k = 1 to infinity



#29
Feb2813, 10:55 AM

P: 642




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