grandes-ecoles 2021 Q9

grandes-ecoles · France · centrale-maths2__psi Sequences and Series Recurrence Relations and Sequence Properties
The Pochhammer symbol is defined, for any real number $a$ and any natural integer $n$, by $$[a]_n = \begin{cases} 1 & \text{if } n = 0 \\ a(a+1)\cdots(a+n-1) = \prod_{k=0}^{n-1}(a+k) & \text{otherwise} \end{cases}$$ If $a$ is a negative or zero integer, justify that the sequence $\left([a]_n\right)_{n \in \mathbb{N}}$ is zero from a certain rank onwards. 
The Pochhammer symbol is defined, for any real number $a$ and any natural integer $n$, by
$$[a]_n = \begin{cases} 1 & \text{if } n = 0 \\ a(a+1)\cdots(a+n-1) = \prod_{k=0}^{n-1}(a+k) & \text{otherwise} \end{cases}$$
If $a$ is a negative or zero integer, justify that the sequence $\left([a]_n\right)_{n \in \mathbb{N}}$ is zero from a certain rank onwards.
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