a. Find a power series representation for
\frac{7}{(5+x)^2}
f(x) =
by recognizing f as the derivative of another function.
(Note that the index variable of the summation is n, it starts at n = 1, and
any coefficient of the summation should be included within the sum itself.)
$\sum_{n=1}^{\infty}$
State the radius of convergence for this power series.
R =
b. Find a power series representation for
\frac{7}{(5+x)^3}
g(x) =
by recognizing g as the derivative of another function.
(Note that the index variable of the summation is n, it starts at n = 2, and
any coefficient of the summation should be included within the sum itself.)
$\sum_{n=2}^{\infty}$
State the radius of convergence for this power series.
R =
c. Find a power series representation for
\frac{7}{(5+x)^4}
h(x) =
by recognizing h as the derivative of another function.
(Note that the index variable of the summation is n, it starts at n = 3, and
any coefficient of the summation should be included within the sum itself.)
$\sum_{n=3}^{\infty}$
State the radius of convergence for this power series.
R =
