Difference between revisions of "009C Sample Midterm 2, Problem 5"

Revision as of 09:33, 5 February 2017

If $\sum _{n=0}^{\infty }c_{n}x^{n}$ converges, does it follow that the following series converges?

a)

\sum _{n=0}^{\infty }c_{n}{\bigg (}{\frac {x}{2}}{\bigg )}^{n}

b)

\sum _{n=0}^{\infty }c_{n}(-x)^{n}

Solution:

(a)

Step 1:

Step 2:

(b)

Final Answer:
(a)
(b)

@@ Line 1: / Line 1: @@
-<span class="exam">
+<span class="exam">If <math>\sum_{n=0}^\infty c_nx^n</math> converges, does it follow that the following series converges?
+::<span class="exam">a) <math>\sum_{n=0}^\infty c_n\bigg(\frac{x}{2}\bigg)^n</math>
+::<span class="exam">b) <math>\sum_{n=0}^\infty c_n(-x)^n </math>
-::<span class="exam">a)
-::<span class="exam">b)