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

Revision as of 22:02, 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 3: / Line 3: @@
 ::::::<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">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>.
+<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>.
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