MHB How Do You Evaluate the Indefinite Integral as a Power Series?

[ajkess1994]

Evaluate the indefinite integral as a power series
∫[ln(1−t)/7t]dt.
Find the first five non-zero terms of power series representation centered at t=0.

Answer: f(t)=

What is the radius of convergence?
Answer: R= 1

Note: Remember to include a constant "C".

This problem has been difficult for me for awhile now. I have my radius but I can't figure out my five f(t) terms it's asking for.
Try to build those terms from this:

(-t^(n))/(7n^(2))

Also n=1

 

[I like Serena]

Evaluate the indefinite integral as a power series
∫[ln(1−t)/7t]dt.
Find the first five non-zero terms of power series representation centered at t=0.

Answer: f(t)=

What is the radius of convergence?
Answer: R= 1

Note: Remember to include a constant "C".

This problem has been difficult for me for awhile now. I have my radius but I can't figure out my five f(t) terms it's asking for.
Try to build those terms from this:

(-t^(n))/(7n^(2))

Also n=1

Hi ajkess1994,

Can you expand $\ln(1−t)$ as a MacLauren series?
Substitute it, and the rest should follow.

 

[ajkess1994]

Yes, Arsen I can expan the ln(1-t) to a MacLauren series, and from there finding the "nth" terms shouldn't be too difficult, thank you for the suggestioon.