fahraynk said: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..
Ha. Good point.Ray Vickson said: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?
The general formula for the power series of integral x/(1-x) is ∑n=0∞ xn+1 = x + x2 + x3 + ... + xn+1 + ...
The coefficients of the power series for integral x/(1-x) can be found using the formula cn = ∫01 xn dx, where cn is the coefficient of xn.
The interval of convergence for the power series of integral x/(1-x) is -1 < x < 1.
The power series for integral x/(1-x) can be used to evaluate the integral by substituting x with the variable of integration and summing the resulting series.
No, the power series for integral x/(1-x) can only be used to approximate the integral for values within the interval of convergence, which is -1 < x < 1.