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CALCULAR LAS SIGUIENTES SUMATORIAS ?

CALCULAR LAS SIGUIENTES SUMATORIAS :

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<img src="https://tex.z-dn.net/?

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Yeimybuendia
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<img src="https://tex.z-dn.net/?f=%5Ctext%7BSea%20%7D%5C%5C%20%5C%5C%0AS%28n%29%3D%5Csum%5Climits_%7Bk%3D1%7D%5En%28-1%29%5E%7Bk%2B1%7D%28k-1%29%5E2%5C%5C%20%5C%5C%0A%5Ctext%7BApliquemos%20la%20ley%20telesc%5C%27opica%20a%20esta%20suma%3A%7D%20%5C%5C%20%5C%5C%0A%5Csum%5Climits_%7Bk%3D1%7D%5En%5Cleft%5B%28-1%29%5E%7B%28k%2B1%29%2B1%7D%5B%28k%2B1%29-1%5D%5E2-%28-1%29%5E%7Bk%2B1%7D%28k-1%29%5E2%5Cright%5D%3D%28-1%29%5E%7Bn%2B2%7Dn%5E2-%28-1%29%5E%7B1%2B1%7D%281-1%29%5E2%5C%5C%20%5C%5C%0A" />

<img src="https://tex.z-dn.net/?f=%5Csum%5Climits_%7Bk%3D1%7D%5En%5Cleft%5B%28-1%29%5E%7Bk%7Dk%5E2%2B%28-1%29%5E%7Bk%7D%28k-1%29%5E2%5Cright%5D%3D%28-1%29%5E%7Bn%7Dn%5E2%5C%5C%20%5C%5C%0A%5Csum%5Climits_%7Bk%3D1%7D%5En%28-1%29%5E%7Bk%7D%5Cleft%5Bk%5E2%2B%28k-1%29%5E2%5Cright%5D%3D%28-1%29%5E%7Bn%7Dn%5E2%5C%5C%20%5C%5C%0A%5Csum%5Climits_%7Bk%3D1%7D%5En%28-1%29%5E%7Bk%7D%5Cleft%5B2k%5E2-2k%2B1%5Cright%5D%3D%28-1%29%5E%7Bn%7Dn%5E2%5C%5C%20%5C%5C%0A%5Cdfrac%7B1%7D%7B2%7D%5Csum%5Climits_%7Bk%3D1%7D%5En%28-1%29%5E%7Bk%7D%5Cleft%5B%282k-1%29%5E2%2B1%5Cright%5D%3D%28-1%29%5E%7Bn%7Dn%5E2%5C%5C%20%5C%5C%0A" />

<img src="https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%5Csum%5Climits_%7Bk%3D1%7D%5En%28-1%29%5E%7Bk%7D%282k-1%29%5E2%2B%20%5Cdfrac%7B1%7D%7B2%7D%5Csum%5Climits_%7Bk%3D1%7D%5En%28-1%29%5E%7Bk%7D%3D%28-1%29%5E%7Bn%7Dn%5E2%5C%5C%20%5C%5C%0A%5Cdfrac%7B1%7D%7B2%7D%5Csum%5Climits_%7Bk%3D1%7D%5En%28-1%29%5E%7Bk%7D%282k-1%29%5E2%2B%20%5Cdfrac%7B%28-1%29%5En-1%7D%7B4%7D%3D%28-1%29%5E%7Bn%7Dn%5E2%5C%5C%20%5C%5C%0A%5Cdfrac%7B1%7D%7B2%7D%5Csum%5Climits_%7Bk%3D1%7D%5En%28-1%29%5E%7Bk%7D%282k-1%29%5E2%3D%28-1%29%5E%7Bn%7D%5Cleft%28n%5E2-%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%2B%5Cdfrac%7B1%7D%7B4%7D%5C%5C%20%5C%5C%0A%5Csum%5Climits_%7Bk%3D1%7D%5En%28-1%29%5E%7Bk%7D%282k-1%29%5E2%3D%28-1%29%5E%7Bn%7D%5Cleft%282n%5E2-%5Cdfrac%7B1%7D%7B2%7D%5Cright%29%2B%5Cdfrac%7B1%7D%7B2%7D%5C%5C%20%5C%5C%0A%5Cboxed%7B%5Csum%5Climits_%7Bk%3D1%7D%5En%28-1%29%5E%7Bk%2B1%7D%282k-1%29%5E2%3D%28-1%29%5E%7Bn%7D%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D-2n%5E2%5Cright%29-%5Cdfrac%7B1%7D%7B2%7D%7D%0A" />.