So I apparently found this doodling around, can anyone prove it?
$$\lim_{x \to \infty} \frac{x}{\frac{\sum_{i=1}^x i }{x}}=2$$
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Please take the time to type out the question. Thank you. – Simply Beautiful Art Dec 14 '16 at 19:35
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1If only I knew how to do it... first time posting here – Otomeram Dec 14 '16 at 19:35
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2=D please check the handbook then! And welcome to the site! – Simply Beautiful Art Dec 14 '16 at 19:36
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I honestly can't understand the limit though. Too many fractions, can you make it more clear? – Simply Beautiful Art Dec 14 '16 at 19:38
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Not only either typing or pasting: put the image straight! – DonAntonio Dec 14 '16 at 19:39
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Its the limit as x approaches infinity of x over (the sum from 1 to x) over x – Otomeram Dec 14 '16 at 19:40
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DonAntonio, 10 reputation required for that – Otomeram Dec 14 '16 at 19:40
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Yet trying to learn the way to type it in tho – Otomeram Dec 14 '16 at 19:41
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http://math.stackexchange.com/questions/2260/proof-for-formula-for-sum-of-sequence-123-ldotsn – Simply Beautiful Art Dec 14 '16 at 19:44
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@Otermeram try viewing my edit to learn a bit of the $\LaTeX$. – Simply Beautiful Art Dec 14 '16 at 19:46
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Yes, thank you so much for that – Otomeram Dec 14 '16 at 19:47
1 Answers
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It seems to be:
$$\cfrac x{\frac{\sum\limits_{i=1}^x i}x}=\frac{x^2}{\frac{x(x+1)}2}\xrightarrow[x\to\infty]{}\frac1{\frac12}=2$$
DonAntonio
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That's really neat. I haven't studied calculus at university yet but I do understand the concept of limits, but since I don't know how to simplify sums and other stuff I couldn't realise about it on my own. Thanks! – Otomeram Dec 14 '16 at 19:44
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