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/sci/ - Science & Math


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4864527 No.4864527 [Reply] [Original]

So what does this series approaches to:
{{ x+(x-1)+(x-2)...+(x-x)}\over n^2 }; x \to ∞
wolfram says to -1/2 how does it calculate it?

>> No.4864575

You have to write that between [m@th][/m@th]

>> No.4864589

multiply it by n^2, then sun it with itself backwards:

top line: x + (x - 1) + (x - 2) + ... + (x - x + 1) + (x - x)
botton line: (x - x) + (x - x + 1) + (x - x + 2) + ... + (x - 1) + x

if you sum the series in the top with the bottom, then notice that if you group it by terms:

[x + (x - x)] + [(x - 1) + (x - x + 1)] + ... [(x - x + 1) + (x - 1)] + [(x - x) + x]

Cancelling out: x * (x + 1) (x terms or however many you have)

Then do x * (x + 1) / 2 (for one line) and you get:

x^2 + x / 2n^2

Therefore if x -> inf, that will go to inf too.

>> No.4864711 [DELETED] 

d'oh i meant
[m@ath]{{ x+(x-1)+(x-2)...+(x-x)}\over x^2 }; x \to ∞[/m@ath]

my bad dunno why i wrote that T_T

>> No.4864715 [DELETED] 

d'oh i meant
[m@ath]{{ x+(x-1)+(x-2)...+(x-x)}\over x^2 }; x \to ∞[/m@th]

my bad dunno why i wrote that T_T

>> No.4864720

d'oh i meant
[m@th]{{ x+(x-1)+(x-2)...+(x-x)}\over x^2 }; x \to ∞[/m@th]

my bad dunno why i wrote that T_T

>> No.4864733
File: 119 KB, 1024x576, 1334884392604.jpg [View same] [iqdb] [saucenao] [google]
4864733

>>4864720
the @ was meant as an 'a' obviously..

>> No.4864742

<span class="math">{{ x+(x-1)+(x-2)...+(x-x)}\over x^2 }; x \to ∞[/spoiler]

>> No.4864771

>>4864742
use \infty for a better infinity sign

>> No.4864783

sry ^^" i'm kinda new here

>> No.4864794

>>4864783
np, if you're into math and taking the effort to learn LaTeX, your presence is incouraged.