Question

Evaluate the derivative:

Answer 1

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

Answer 2

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

Answer 3

not used to x with n xD

Answer 4

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

Answer 5

xD

Answer 6

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

Answer 7

oh this makes more sense

Answer 8

.