Sa se calculeze ∑ Vedeti in imagine CINE MA POATE AJUTA DAU COROANA !!!
Anexe:
marcela16:
Nu știu. Este de liceu?
Da
băieții mei sunt mai mici, altfel te ajuta
... Nici eu nu stiu ce sa i fac
uită - te la utilizatori și vezi care este bun la mate. roaga-i sa te ajute
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4
Salut,
![S=\sum\limits_{k=1}^n(n-k)\cdot A_n^{k-1}=\sum\limits_{k=1}^n(n-k)\dfrac{n!}{(n-k+1)!}=n!\cdot\sum\limits_{k=1}^n\dfrac{n-k+1-1}{(n-k+1)!}=\\\\=n!\cdot\sum\limits_{k=1}^n\left[\dfrac{n-k+1}{(n-k+1)!}-\dfrac{1}{(n-k+1)!}\right]=n!\cdot\sum\limits_{k=1}^n\left[\dfrac{n-k+1}{(n-k+1)(n-k)!}-\dfrac{1}{(n-k+1)!}\right]=\\\\=n!\cdot\sum\limits_{k=1}^n\left[\dfrac{1}{(n-k)!}-\dfrac{1}{(n-k+1)!}\right].\ Not\breve{a}m\ cu\ S_1=\sum\limits_{k=1}^n\left[\dfrac{1}{(n-k)!}-\dfrac{1}{(n-k+1)!}\right].\\\\S_1=\dfrac{1}{(n-1)!}-\dfrac{1}{n!}+\\\\+\dfrac{1}{(n-2)!}-\dfrac{1}{(n-1)!}+\\\\+\dfrac{1}{(n-3)!}-\dfrac{1}{(n-2)!}+\\\\+\ldots+\\\\+\dfrac{1}{1!}-\dfrac{1}{2!}+\\\\+\dfrac{1}{0!}-\dfrac{1}{1!}=1-\dfrac{1}{n!}.\\\\Suma\ din\ enun\c{t}\ S=n!\cdot S_1=n!-1.](https://tex.z-dn.net/?f=S%3D%5Csum%5Climits_%7Bk%3D1%7D%5En%28n-k%29%5Ccdot+A_n%5E%7Bk-1%7D%3D%5Csum%5Climits_%7Bk%3D1%7D%5En%28n-k%29%5Cdfrac%7Bn%21%7D%7B%28n-k%2B1%29%21%7D%3Dn%21%5Ccdot%5Csum%5Climits_%7Bk%3D1%7D%5En%5Cdfrac%7Bn-k%2B1-1%7D%7B%28n-k%2B1%29%21%7D%3D%5C%5C%5C%5C%3Dn%21%5Ccdot%5Csum%5Climits_%7Bk%3D1%7D%5En%5Cleft%5B%5Cdfrac%7Bn-k%2B1%7D%7B%28n-k%2B1%29%21%7D-%5Cdfrac%7B1%7D%7B%28n-k%2B1%29%21%7D%5Cright%5D%3Dn%21%5Ccdot%5Csum%5Climits_%7Bk%3D1%7D%5En%5Cleft%5B%5Cdfrac%7Bn-k%2B1%7D%7B%28n-k%2B1%29%28n-k%29%21%7D-%5Cdfrac%7B1%7D%7B%28n-k%2B1%29%21%7D%5Cright%5D%3D%5C%5C%5C%5C%3Dn%21%5Ccdot%5Csum%5Climits_%7Bk%3D1%7D%5En%5Cleft%5B%5Cdfrac%7B1%7D%7B%28n-k%29%21%7D-%5Cdfrac%7B1%7D%7B%28n-k%2B1%29%21%7D%5Cright%5D.%5C+Not%5Cbreve%7Ba%7Dm%5C+cu%5C+S_1%3D%5Csum%5Climits_%7Bk%3D1%7D%5En%5Cleft%5B%5Cdfrac%7B1%7D%7B%28n-k%29%21%7D-%5Cdfrac%7B1%7D%7B%28n-k%2B1%29%21%7D%5Cright%5D.%5C%5C%5C%5CS_1%3D%5Cdfrac%7B1%7D%7B%28n-1%29%21%7D-%5Cdfrac%7B1%7D%7Bn%21%7D%2B%5C%5C%5C%5C%2B%5Cdfrac%7B1%7D%7B%28n-2%29%21%7D-%5Cdfrac%7B1%7D%7B%28n-1%29%21%7D%2B%5C%5C%5C%5C%2B%5Cdfrac%7B1%7D%7B%28n-3%29%21%7D-%5Cdfrac%7B1%7D%7B%28n-2%29%21%7D%2B%5C%5C%5C%5C%2B%5Cldots%2B%5C%5C%5C%5C%2B%5Cdfrac%7B1%7D%7B1%21%7D-%5Cdfrac%7B1%7D%7B2%21%7D%2B%5C%5C%5C%5C%2B%5Cdfrac%7B1%7D%7B0%21%7D-%5Cdfrac%7B1%7D%7B1%21%7D%3D1-%5Cdfrac%7B1%7D%7Bn%21%7D.%5C%5C%5C%5CSuma%5C+din%5C+enun%5Cc%7Bt%7D%5C+S%3Dn%21%5Ccdot+S_1%3Dn%21-1. "S=\sum\limits_{k=1}^n(n-k)\cdot A_n^{k-1}=\sum\limits_{k=1}^n(n-k)\dfrac{n!}{(n-k+1)!}=n!\cdot\sum\limits_{k=1}^n\dfrac{n-k+1-1}{(n-k+1)!}=\\\\=n!\cdot\sum\limits_{k=1}^n\left[\dfrac{n-k+1}{(n-k+1)!}-\dfrac{1}{(n-k+1)!}\right]=n!\cdot\sum\limits_{k=1}^n\left[\dfrac{n-k+1}{(n-k+1)(n-k)!}-\dfrac{1}{(n-k+1)!}\right]=\\\\=n!\cdot\sum\limits_{k=1}^n\left[\dfrac{1}{(n-k)!}-\dfrac{1}{(n-k+1)!}\right].\ Not\breve{a}m\ cu\ S_1=\sum\limits_{k=1}^n\left[\dfrac{1}{(n-k)!}-\dfrac{1}{(n-k+1)!}\right].\\\\S_1=\dfrac{1}{(n-1)!}-\dfrac{1}{n!}+\\\\+\dfrac{1}{(n-2)!}-\dfrac{1}{(n-1)!}+\\\\+\dfrac{1}{(n-3)!}-\dfrac{1}{(n-2)!}+\\\\+\ldots+\\\\+\dfrac{1}{1!}-\dfrac{1}{2!}+\\\\+\dfrac{1}{0!}-\dfrac{1}{1!}=1-\dfrac{1}{n!}.\\\\Suma\ din\ enun\c{t}\ S=n!\cdot S_1=n!-1.")
Green eyes.
Green eyes.
Genial~!
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