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Working with indefinite number of variables


Hi,
I have been wrapping my head around this for a while now and I have not found a solution so far.
I want to work with an indefinite number of variables in mathematica and use some built in functions.

To make things more specific for starters I want to do the following:

Define a sum with n summands each containing a new variable x[i] (in the i-th summand): 
sum[n_] = Sum[i*x[i], {i, 1, n}]

Then I want to differentiate the expression with respect to some x[i] like: 
D[sum[n],x[2]]

Mathematica return 0 instead of 2. If I supply a specific n like: 
D[sum[2],x[2]]
everything works fine.

I thought about using Assumptions for n, but with no success so far.

How can I do that right?



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