## Empty one year ago Evaluate the derivative:

1. Empty

$\frac{d}{dn} \left( \sum_{k=0}^n x^k \right)$

2. anonymous

now the thing is should i consider x as constant or variable of n ?

3. anonymous

not used to x with n xD

4. anonymous

$$\Large \frac{d}{dn} \left( \sum_{k=0}^n x^k \right) \\ \Large \sum_{k=0}^n x^k =\dfrac{1+x^n}{1-x}\\ \Large \dfrac{d}{dn} \left( \dfrac{1+x^n}{1-x} \right)$$

5. anonymous

xD

6. Empty

We could do something like this: $\frac{S(n+1)-S(n)}{(n+1)-n} = \frac{\sum_{k=0}^{n+1} x^k - \sum_{k=0}^n x^k}{1} = x^{n+1}$

7. anonymous

oh this makes more sense

8. IrishBoy123

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