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^n = \sum_{k = 0}^n {n \choose k}z^k[/tex]](images/latex/bd7068c5c567dc0c8fd064bd229f03102f65e656_0.png "[tex](1 + z)^n = \sum_{k = 0}^n {n \choose k}z^k[/tex]")
, aplicás las operaciones que piden así:
![[tex]z \frac{d}{dz}(1 + z)^n = z \frac{d}{dz} \left [ \sum_{k = 0}^n {n \choose k} z^k \right ] = \sum_{k = 0}^n {n \choose k} z \frac{dz^k}{dz}[/tex]](images/latex/82883de99f735a3b6988df659c1fa4e70a512266_0.png "[tex]z \frac{d}{dz}(1 + z)^n = z \frac{d}{dz} \left [ \sum_{k = 0}^n {n \choose k} z^k \right ] = \sum_{k = 0}^n {n \choose k} z \frac{dz^k}{dz}[/tex]")
![[tex]z^2 \frac{d^2}{dz^2}(1 + z)^n = z^2 \frac{d^2}{dz^2} \left [\sum_{k = 0}^n {n \choose k} z^k \right ] = \sum_{k = 0}^n {n \choose k} z^2 \frac{d^2z^k}{dz^2}[/tex]](images/latex/9806288d09e068f6b0cfe7457866b4a8fa21df79_0.png "[tex]z^2 \frac{d^2}{dz^2}(1 + z)^n = z^2 \frac{d^2}{dz^2} \left [\sum_{k = 0}^n {n \choose k} z^k \right ] = \sum_{k = 0}^n {n \choose k} z^2 \frac{d^2z^k}{dz^2}[/tex]")
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