Calc 3 question

[sportlover36]

how can i find a power series representation for a function like f(x)= ln(1+7x)?

 

[Mark44]

how can i find a power series representation for a function like f(x)= ln(1+7x)?

There are at least two ways. One is very mechanical and involves taking the derivatives of your fucntion. The other is probably a lot quicker. Can you find a power series for 7/(1 + 7x) = 1/(x + 1/7)? What's the connection between ln(1 + 7x) and 1/(x + 1/7)?

 

[sportlover36]

Im not really sure what the connection is but i got this at the answer...the sumation from n=1 to infinity -7x^n/n

 

[Mark44]

The connection is that d/dx(ln(1 + 7x) = 7/(1 + 7x), or conversely, that ln(1 + 7x) = $\int$7/(1 + 7x) dx.

If you didn't understand that connection, how did you get the result that you got? BTW, I'm not sure that your result is right.