Thread: power series representation #2

Evaluate the indefinite integral as a series:



Here is what I did:





So, what do I do now? Since I differentiated to get , do I just need to integrate it now and then multiply back in? Did I miss anything ?

Originally Posted by mollymcf2009

Evaluate the indefinite integral as a series:



Here is what I did:





So, what do I do now? Since I differentiated to get , do I just need to integrate it now and then multiply back in? Did I miss anything ?

and exactly why would you factor a function of t out of a dt-integral? you can only factor out constants (with respect to the variable of integration) remember?

Hint: you know the power series for the given log function, just write that in. then divide it through by t. then integrate term by term. well, that's not really a hint, that's how to do the problem

by the way, your power series for the log is incorrect, you wrote the power series for 1/(1 - t) ...which is NOT the integral of ln(1 - t), by the way

Originally Posted by Jhevon

and exactly why would you factor a function of t out of a dt-integral? you can only factor out constants (with respect to the variable of integration) remember?

Hint: you know the power series for the given log function, just write that in. then divide it through by t. then integrate term by term. well, that's not really a hint, that's how to do the problem

by the way, your power series for the log is incorrect, you wrote the power series for 1/(1 - t) ...which is NOT the integral of ln(1 - t), by the way

Ok, so what I would have for my power series is:
?

Is that what you said for me to do?

Originally Posted by mollymcf2009

Ok, so what I would have for my power series is:
?

Is that what you said for me to do?

question: what does the power series for ln(1 - t) look like? did you use that here?