Question

is this lagrange? i dont even know test tomorrow HALP!!
If f(x)= sum ((2x)^(k+1))/(k+1) then what is f'(-1/3)? I have some ideas, but what am i doing wrong?

Answer 1

ok so for f'(x) i got 2+4x+x^2+16x^3....2(2x)^k for general term

Answer 2

so do you just plug in (-1/3) into that equation?

Answer 3

is f defined as
\[
f(x)=\sum
_{k=0}^{\infty }
\frac{2^{k+1} x^{k+1}}{k+1}
\]

Answer 4

\[
f'(x)=\sum _{k=0}^{\infty } 2^{k+1}
x^k
\]

Answer 5

\[
f'(-1/3)=\sum _{k=0}^{\infty } 2^{k+1}
\left(-\frac{1}{3}\right)^k
=\frac{6}{5}
\]