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# Summation notation of a sequence

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I am so bad at identifying it.

The sequence of 7 + 14x + 42x^2 + 168x^3 + 840x^4 +.....

n=0, and goes to infinity

I know that it has (x)^n

I see 7x2, 14x3, 42x4, 168x5, but I am having trouble wiritng it down as summation notation.

Nov 18, 2020

### 1+0 Answers

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Summation notation of a sequence
The sequence of $$7 + 14x + 42x^2 + 168x^3 + 840x^4 + \ldots$$
$$n=0$$, and goes to infinity.

$$\begin{array}{|rcll|} \hline && \mathbf{ 7 + 14x + 42x^2 + 168x^3 + 840x^4 + \ldots} \\ && \boxed{7 = 7\cdot 1!\\ 14 = 7\cdot 2!\\ 42 = 7\cdot 3!\\ 168 = 7\cdot 4!\\ 840 = 7\cdot 5!\\ \ldots } \\ &=& 7\cdot 1! + 7\cdot 2!x + 7\cdot 3!x^2 + 7\cdot 4!x^3 + 7\cdot 5!x^4 + \ldots \\ &=& \mathbf{ 7\sum \limits_{n=0}^{\infty} (n+1)!x^n} \\ \hline \end{array}$$

Nov 19, 2020