Converting 1/(1+7x)^2 into a Power Series

[aces9113]

Homework Statement

i need to make the function 1/(1+7x)^2 into a power series that goes from n=1 to infinity. I know that i have to get the answer through differentiating because the for the previous problem, i found that the function 7/(1+7x) resulted in ( -1 )^n* 7*7^n*x^n when n=0 to infinity

Homework Equations

The Attempt at a Solution

I know that as 1/(1-x) equals x^n and 1/(1-x)^2 equals n*x^(n-1) when n begins at 1 so i tried to use that. my previous try was (1)^n*(-1)*x^(n-1)*7^(2n-1)*(n). I'm on my last try and I really need help!

 

[Chantry]

f = 1/(1+7x)
f' = -7/(1 + 7x)^2

General formula for series:
1/(1-x) = sum[0-->infinite](x^n)

So, 1/(1-(-7x)) = sum[0-->infinite]((-7x)^n) = sum[0-->infinite]((-1)^n(7x)^n)

Now, just take the derivative of the summation, and you should get your answer.
Also, you'll have to find a way to get that -7 into the summ ;).

 

[aces9113]

thank you so much! that was incredibly helpful