Changes

  == [[Propriedades de Somatório ==    <math> \sum_{n=s}^t C\cdot f(n) = C\cdot \sum_{n=s}^t f(n) </math>onde C é uma constante.  <math> \sum_{n=s}^t f(n) + \sum_{n=s}^{t} g(n) = \sum_{n=s}^t \left[f(n) + g(n)\right] </math> <math> \sum_{n=s}^t f(n) - \sum_{n=s}^{t} g(n) = \sum_{n=s}^t \left[f(n) - g(n)\right] </math> <math> \sum^n_{i = m} f(i) = \sum^{n+p}_{i = m+p} f(i-p) </math> <math> \sum\limits_{n=s}^{t} j = \sum\limits_{n=1}^{t} j - \sum\limits_{n=1}^{s-1} j </math> <math> \sum_{n=s}^j f(n) + \sum_{n=j+1}^t f(n) = \sum_{n=s}^t f(n)</math>, note que <math> s \leq j \leq t </math> <math> \sum_{i=m}^n i = \frac{n(n+1)}{2} - \frac{m(m-1)}{2} = \frac{(n+1-m)(n+m)}{2},</math> progressão aritmética. <math> \sum_{i=0}^n i = \sum_{i=1}^n i = \frac{n(n+1)}{2} </math> <math> \sum\limits_{k=0}^{n-1}{2^k} = 2^n-1 </math> <math> \sum_{i=s}^m\sum_{j=t}^n {a_i}{c_j} = \sum_{i=s}^m a_i \cdot \sum_{j=t}^n c_j </math> <math> \sum_{i=0}^n i^3 = \left(\sum_{i=0}^n i\right)^2 </math> <math> \sum_{i=m}^{n-1} a^i = \frac{a^m-a^n}{1-a} (m < n) </math> <math> \sum_{i=0}^{n-1} a^i = \frac{1-a^n}{1-a} </math>