Difference between revisions of "009C Sample Final 1, Problem 5"

Revision as of 20:09, 1 February 2016

Let

f(x)=\sum _{n=1}^{\infty }nx^{n}

a) Find the radius of convergence of the power series.

b) Determine the interval of convergence of the power series.

c) Obtain an explicit formula for the function

f(x)

.

Foundations:

Solution:

(a)

(b)

Step 2:

Step 3:

(c)

Step 1:

@@ Line 1: / Line 1: @@
+<span class="exam"> Let
+::::::<math>f(x)=\sum_{n=1}^{\infty} nx^n</math>
+::<span class="exam">a) Find the radius of convergence of the power series.
+::<span class="exam">b) Determine the interval of convergence of the power series.
+::<span class="exam">c) Obtain an explicit formula for the function <math>f(x)</math>.
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Foundations: &nbsp;