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Научный форум dxdyМатематика, Физика, Computer Science, Machine Learning, LaTeX, Механика и Техника, Химия,Биология и Медицина, Экономика и Финансовая Математика, Гуманитарные науки |
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| Страница 1 из 1 |
[ Сообщений: 2 ] |
21.11.2007, 12:07 
![\[
1 - \frac{1}
{2}
\]](https://dxdy-03.korotkov.co.uk/f/2/6/3/26301545deaf44c22437dc6fadd8970f82.png "\[
1 - \frac{1}
{2}
\]")
![\[
1 - \frac{1}
{2} - \frac{1}
{3} + \frac{1}
{6}
\]](https://dxdy-03.korotkov.co.uk/f/e/3/6/e3622ec16064b1742e2ae945dd79154d82.png "\[
1 - \frac{1}
{2} - \frac{1}
{3} + \frac{1}
{6}
\]")
![\[
1 - \frac{1}
{2} - \frac{1}
{3} + \frac{1}
{6} - \frac{1}
{5} + \frac{1}
{{10}} + \frac{1}
{{15}} - \frac{1}
{{30}}
\]](https://dxdy-04.korotkov.co.uk/f/f/e/7/fe75d01694566053f9e6fdf09e4a13b482.png "\[
1 - \frac{1}
{2} - \frac{1}
{3} + \frac{1}
{6} - \frac{1}
{5} + \frac{1}
{{10}} + \frac{1}
{{15}} - \frac{1}
{{30}}
\]")
![\[
1 - \frac{1}
{2} - \frac{1}
{3} + \frac{1}
{6} - \frac{1}
{5}\left( {1 - \frac{1}
{2} - \frac{1}
{3} + \frac{1}
{6}} \right)
\]](https://dxdy-04.korotkov.co.uk/f/3/1/e/31e2b71a08844652cffddbc6a319e45b82.png "\[
1 - \frac{1}
{2} - \frac{1}
{3} + \frac{1}
{6} - \frac{1}
{5}\left( {1 - \frac{1}
{2} - \frac{1}
{3} + \frac{1}
{6}} \right)
\]")
![\[
\left( {1 - \frac{1}
{2} - \frac{1}
{3} + \frac{1}
{6}} \right) \cdot \left( {1 - \frac{1}
{5}} \right)
\]](https://dxdy-01.korotkov.co.uk/f/c/6/4/c642f80e20d173d430b1332de2f1d85282.png "\[
\left( {1 - \frac{1}
{2} - \frac{1}
{3} + \frac{1}
{6}} \right) \cdot \left( {1 - \frac{1}
{5}} \right)
\]")
![\[
\left[ {1 - \frac{1}
{2} - \frac{1}
{3}\left( {1 - \frac{1}
{2}} \right)} \right] \cdot \left( {1 - \frac{1}
{5}} \right)
\]](https://dxdy-02.korotkov.co.uk/f/1/0/8/108c2347ba6f815a8836f954ba7b129d82.png "\[
\left[ {1 - \frac{1}
{2} - \frac{1}
{3}\left( {1 - \frac{1}
{2}} \right)} \right] \cdot \left( {1 - \frac{1}
{5}} \right)
\]")
![\[
\left[ {\left( {1 - \frac{1}
{2}} \right) \cdot \left( {1 - \frac{1}
{3}} \right)} \right] \cdot \left( {1 - \frac{1}
{5}} \right)
\]](https://dxdy-03.korotkov.co.uk/f/a/6/c/a6ccad0ce77671b8bced81b6a3142ba482.png "\[
\left[ {\left( {1 - \frac{1}
{2}} \right) \cdot \left( {1 - \frac{1}
{3}} \right)} \right] \cdot \left( {1 - \frac{1}
{5}} \right)
\]")
![\[
\frac{1}
{2} \cdot \frac{2}
{3} \cdot \frac{4}
{5}.....\frac{{(p_k - 1)\# }}
{{p_k }}
\]](https://dxdy-04.korotkov.co.uk/f/f/e/9/fe94f0c2fe8b8fd58f3772705181a5e582.png "\[
\frac{1}
{2} \cdot \frac{2}
{3} \cdot \frac{4}
{5}.....\frac{{(p_k - 1)\# }}
{{p_k }}
\]")
![\[
p_k = 2;k = 1
\]](https://dxdy-01.korotkov.co.uk/f/8/4/7/847ef4793f2603a87957ada2665c3d4882.png "\[
p_k = 2;k = 1
\]")
![\[
p_k = 3;k = 2
\]](https://dxdy-04.korotkov.co.uk/f/7/1/e/71e275cdd15cb760f0fb09a37d8cae6682.png "\[
p_k = 3;k = 2
\]")
![\[
p_k = 11;k = 5;
\]](https://dxdy-03.korotkov.co.uk/f/6/8/8/6885b148f62ad29d49be71956f741f2982.png "\[
p_k = 11;k = 5;
\]")
![\[
\pi (p_k ,p_k^2 ) = p_k^2 \cdot \frac{{(p_k - 1)\# }}
{{p_k \# }}
\]](https://dxdy-02.korotkov.co.uk/f/1/b/4/1b4b837d1ee5843baf7474905470718782.png "\[
\pi (p_k ,p_k^2 ) = p_k^2 \cdot \frac{{(p_k - 1)\# }}
{{p_k \# }}
\]")
![\[
\pi (p_k^2 ,p_{k + 1}^2 ) = \left( {p_{k + 1}^2 \cdot \frac{{(p_{k + 1} - 1)\# }}
{{(p_{k + 1} )\# }}} \right) - \left( {p_k^2 \cdot \frac{{(p_k - 1)\# }}
{{(p_k )\# }}} \right)
\]](https://dxdy-04.korotkov.co.uk/f/7/3/f/73fb61c09f17830c4111d800cace545682.png "\[
\pi (p_k^2 ,p_{k + 1}^2 ) = \left( {p_{k + 1}^2 \cdot \frac{{(p_{k + 1} - 1)\# }}
{{(p_{k + 1} )\# }}} \right) - \left( {p_k^2 \cdot \frac{{(p_k - 1)\# }}
{{(p_k )\# }}} \right)
\]")
![\[
\pi (0,p_{k + 1}^2 ) = \sum\limits_{k = 1}^\infty {\left[ {\left( {p_{k + 1}^2 \cdot \frac{{(p_{k + 1} - 1)\# }}
{{(p_{k + 1} )\# }}} \right) - \left( {p_k^2 \cdot \frac{{(p_k - 1)\# }}
{{(p_k )\# }}} \right)} \right]}
\]](https://dxdy-01.korotkov.co.uk/f/c/d/5/cd50bb2d00af0106e9ba462a6a26686482.png "\[
\pi (0,p_{k + 1}^2 ) = \sum\limits_{k = 1}^\infty {\left[ {\left( {p_{k + 1}^2 \cdot \frac{{(p_{k + 1} - 1)\# }}
{{(p_{k + 1} )\# }}} \right) - \left( {p_k^2 \cdot \frac{{(p_k - 1)\# }}
{{(p_k )\# }}} \right)} \right]}
\]")
![\[
\pi (0,n) = \sum\limits_{k = 1}^\infty {\left[ {\left( {p_k^2 \cdot \frac{{(p_k - 1)\# }}
{{(p_k )\# }}} \right) - \left( {p_{k - 1}^2 \cdot \frac{{(p_{k - 1} - 1)\# }}
{{(p_{k - 1} )\# }}} \right)} \right]} + (n - p_k^2 ) \cdot \frac{{(p_k - 1)\# }}
{{p_k \# }}
\]](https://dxdy-01.korotkov.co.uk/f/8/2/a/82afe7c323406e80d11c067d4361bd2182.png "\[
\pi (0,n) = \sum\limits_{k = 1}^\infty {\left[ {\left( {p_k^2 \cdot \frac{{(p_k - 1)\# }}
{{(p_k )\# }}} \right) - \left( {p_{k - 1}^2 \cdot \frac{{(p_{k - 1} - 1)\# }}
{{(p_{k - 1} )\# }}} \right)} \right]} + (n - p_k^2 ) \cdot \frac{{(p_k - 1)\# }}
{{p_k \# }}
\]")
![\[
p_k^2 \leqslant n < p_{k + 1}^2
\]](https://dxdy-01.korotkov.co.uk/f/8/4/f/84f1817a4b35ee7806e2a67ab864e37382.png "\[
p_k^2 \leqslant n < p_{k + 1}^2
\]")
