Sample Questions And Detailed Answers On Infinite Series
3 views 0 purchase
Course
Infinite Series
Institution
Infinite Series
Book
A Student\'s Guide to Infinite Series and Sequences
Well organised and structured to make every student understand Infinite series through questions and answers , the study guide book will also help you comprehend it practically.
Here are solved sample
questions on infinite series:
1. Determine whether the series
∑ (n=1 to ∞) 1/n^2 converges or
diverges.
Solution:
We can use the p-series test to
determine whether this series
converges or diverges. The p-
series test states that if ∑ 1/n^p
converges, then ∑ 1/n also
converges for p > 1, and
diverges for p ≤ 1.
In this case, p = 2, which is
greater than 1. Therefore, we
can apply the p-series test and
,conclude that the series ∑ 1/n^2
converges.
2. Find the sum of the infinite
series ∑ (n=0 to ∞) 2^n.
,Solution:
We can use the formula for the
sum of an infinite geometric
series to find the sum of this
series. The formula states that if
a is the first term and r is the
common ratio, then the sum of
the infinite series is S = a/(1-r).
In this case, a = 1 (since 2^0 = 1)
and r = 2. Therefore,
S = 1/(1-2) = -1
So the sum of the infinite series
∑ 2^n is -1.
3. Determine whether the series
∑ (n=1 to ∞) (-1)^n/√n converges
, or diverges.
Solution:
We can use the alternating
series test to determine whether
this series converges
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller goodthoughtsqweku. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $17.99. You're not tied to anything after your purchase.