# How do you find the power series for #f'(x)# and #int f(t)dt# from [0,x] given the function #f(x)=Sigma (n+1)/nx^n# from #n=[1,oo)#?

We have:

And so:

And:

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To find the power series for ( f'(x) ) and ( \int f(t) , dt ) from ( [0,x] ) given the function ( f(x) = \sum_{n=1}^{\infty} \frac{n+1}{nx^n} ) from ( n=[1,\infty) ):

- Differentiate the given function term by term to find ( f'(x) ).
- Integrate the given function term by term to find ( \int f(t) , dt ) from ( [0,x] ).

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