Mircea Merca's conjecteture
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Mircea Merca conjectured that $$left lfloor{frac{1}{n}sum_{k=1}^nsqrt{k}}right rfloor=left lfloor{left(frac{2}{3}+frac{1}{6n}right)sqrt{n+1}}right rfloor$$
John Zacharias claimed that he had proved this conjecture in this article. Did he actually prove the conjecture? How can I find the related article?
sequences-and-series floor-function
asked Nov 17 at 23:34
Larry
1,1892622
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Mircea Merca conjectured that $$left lfloor{frac{1}{n}sum_{k=1}^nsqrt{k}}right rfloor=left lfloor{left(frac{2}{3}+frac{1}{6n}right)sqrt{n+1}}right rfloor$$
John Zacharias claimed that he had proved this conjecture in this article. Did he actually prove the conjecture? How can I find the related article?
sequences-and-series floor-function
asked Nov 17 at 23:34
Larry
1,1892622
2
The asymptotic behaviour of $H_n^{(1/2)}$ can be found by summation by parts or creative telescoping. This is more a challenging exercise in Calculus than a ground-breaking conjecture.
– Jack D'Aurizio
Nov 18 at 0:04
1
This is OEIS sequence A300287 which has a link to Thomas P. Wihler, arXiv:1803.00362.
– Somos
Nov 18 at 0:18
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Mircea Merca conjectured that $$left lfloor{frac{1}{n}sum_{k=1}^nsqrt{k}}right rfloor=left lfloor{left(frac{2}{3}+frac{1}{6n}right)sqrt{n+1}}right rfloor$$
John Zacharias claimed that he had proved this conjecture in this article. Did he actually prove the conjecture? How can I find the related article?
sequences-and-series floor-function
asked Nov 17 at 23:34
Larry
1,1892622
Mircea Merca conjectured that $$left lfloor{frac{1}{n}sum_{k=1}^nsqrt{k}}right rfloor=left lfloor{left(frac{2}{3}+frac{1}{6n}right)sqrt{n+1}}right rfloor$$
John Zacharias claimed that he had proved this conjecture in this article. Did he actually prove the conjecture? How can I find the related article?
sequences-and-series floor-function
sequences-and-series floor-function
asked Nov 17 at 23:34
Larry
1,1892622
asked Nov 17 at 23:34
Larry
1,1892622
asked Nov 17 at 23:34
Larry
1,1892622
asked Nov 17 at 23:34
Larry
1,1892622
asked Nov 17 at 23:34
Larry
1,1892622
1,1892622
2
The asymptotic behaviour of $H_n^{(1/2)}$ can be found by summation by parts or creative telescoping. This is more a challenging exercise in Calculus than a ground-breaking conjecture.
– Jack D'Aurizio
Nov 18 at 0:04
1
This is OEIS sequence A300287 which has a link to Thomas P. Wihler, arXiv:1803.00362.
– Somos
Nov 18 at 0:18
add a comment |
2
The asymptotic behaviour of $H_n^{(1/2)}$ can be found by summation by parts or creative telescoping. This is more a challenging exercise in Calculus than a ground-breaking conjecture.
– Jack D'Aurizio
Nov 18 at 0:04
1
This is OEIS sequence A300287 which has a link to Thomas P. Wihler, arXiv:1803.00362.
– Somos
Nov 18 at 0:18
2
2
The asymptotic behaviour of $H_n^{(1/2)}$ can be found by summation by parts or creative telescoping. This is more a challenging exercise in Calculus than a ground-breaking conjecture.
– Jack D'Aurizio
Nov 18 at 0:04
The asymptotic behaviour of $H_n^{(1/2)}$ can be found by summation by parts or creative telescoping. This is more a challenging exercise in Calculus than a ground-breaking conjecture.
– Jack D'Aurizio
Nov 18 at 0:04
1
1
This is OEIS sequence A300287 which has a link to Thomas P. Wihler, arXiv:1803.00362.
– Somos
Nov 18 at 0:18
This is OEIS sequence A300287 which has a link to Thomas P. Wihler, arXiv:1803.00362.
– Somos
Nov 18 at 0:18
add a comment |
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2
The asymptotic behaviour of $H_n^{(1/2)}$ can be found by summation by parts or creative telescoping. This is more a challenging exercise in Calculus than a ground-breaking conjecture.
– Jack D'Aurizio
Nov 18 at 0:04
1
This is OEIS sequence A300287 which has a link to Thomas P. Wihler, arXiv:1803.00362.
– Somos
Nov 18 at 0:18