Integral x/(1-x) via power series?

[fahraynk]

So, ∫x/(1-x)... can I solve this as a power series

∫(x*Σ x^n) = ∫(Σ x^(n+1))= (1/(n+2)*Σ x^(n+2))?

Is this correct? I know there is other ways to do it... But should this be correct on a test? This solution is more fun..

 

[Ray Vickson]

So, ∫x/(1-x)... can I solve this as a power series

∫(x*Σ x^n) = ∫(Σ x^(n+1))= (1/(n+2)*Σ x^(n+2))?

Is this correct? I know there is other ways to do it... But should this be correct on a test? This solution is more fun..

More fun than what? More fun than the exact expression? Is a solution of limited applicability (i.e., is correct only for limited values of x) preferable to one that applies to all x ≠ 1?

 

[fahraynk]

More fun than what? More fun than the exact expression? Is a solution of limited applicability (i.e., is correct only for limited values of x) preferable to one that applies to all x ≠ 1?

Ha. Good point.