Math & Data Science Q&A - Get answers from our AI that are verified by human experts
First time here? Checkout the FAQs!

*Math Image Search only works best with zoomed in and well cropped math screenshots. Check DEMO

0 like 0 dislike
I(x)= \begin{cases}0 & (x \leq 0) \\ 1 & (x>0)\end{cases}
if \(\left\{x_{n}\right\}\) is a sequence of distinct points of \((a, b)\), and if \(\sum\left|c_{n}\right|\) converges, prove that the series
f(x)=\sum_{n=1}^{\infty} c_{n} I\left(x-x_{n}\right) \quad(a \leq x \leq b)
converges uniformly, and that \(f\) is continuous for every \(x \neq x_{n}\).
in Mathematics by Diamond (71,587 points) | 67 views

1 Answer

0 like 0 dislike
Best answer
The uniform convergence is a consequence of the \(M\)-test with \(M_{n}=\) \(\left|c_{n}\right|\). Hence \(f\) is continuous wherever each of the individual terms is continuous, in particular, at least for \(x \neq x_{n}\).
by Diamond (71,587 points)

Related questions

0 like 0 dislike
1 answer
0 like 0 dislike
0 answers

Join MathsGee, where you get expert-verified math and data science education support from our community fast.

On the MathsGee, you can:

1. Ask and answer questions

2. Get expert-verified answers

3. Vote on questions and answers

4. Tip your favorite community members

5. Join expert live video sessions (Paid/Free)

6. Earn points by participating

7. Start a Fundraiser

Posting on MathsGee

1. Remember the human

2. Act like you would in real life

3. Find original source of content

4. Check for duplicates before publishing

5. Read the community guidelines

MathsGee Rules

1. Answers to questions will be posted immediately after moderation

2. Questions will be queued for posting immediately after moderation

3. Depending on the number of messages we receive, you could wait up to 24 hours for your message to appear. But be patient as posts will appear after passing our moderation.

MathsGee Android Q&A

MathsGee Android Q&A