Ejercicios de Sumatoria

 

 

 

 

 

1) Hallar los valores numéricos de las siguientes

$\displaystyle\sum_{i=1}^{500} (i^2+1)^2 = $

 

  $\displaystyle\sum_{i=5}^{30} (i^3-4)j = $

 

$\displaystyle\sum_{i=-2}^{80} i(i+3)^2 = $

 

$\displaystyle\sum_{i=-4}^{6} \frac{k}{k+2} = $

 

 

Establecer si las siguientes propiedades son verdaderas:

 

 

$\displaystyle\sum_{i=1}^{n} C = nC $

$\displaystyle\sum_{i=1}^{n} i = \frac{n(n+1)}{2} $

 

$\displaystyle\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}$

 

$\displaystyle\sum_{i=1}^{n} i^3 = \frac{n^2(n+1)^2}{4} $

 

$\displaystyle\sum_{i=1}^{n} i^4 = \frac{n(n+1)(6n^3 + 9n^2+n - 1)}{30} $

 

$\displaystyle\sum_{i=1}^{n}(a_i - a_{i-1}) = a_n - a_0$

 

$\displaystyle\sum_{i=1}^{n} 10^{i+1}-10^i =$

 

Encuentre el número n tal que:

$\displaystyle\sum_{i=1}^{n} i = 78 $

 

$\displaystyle\sum_{i=1}^{n} \frac{2i^2}{n(n+1)} = 305 $

 

 

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