Podcast
Play an AI-generated podcast conversation about this lesson
Questions and Answers
Which of the following statements about the series 1 + 2 + 3 + 4 + ⋯ is true?
Which of the following statements about the series 1 + 2 + 3 + 4 + ⋯ is true?
- The series is equal to 0
- The series is divergent (correct)
- The series is convergent
- The series has a finite sum
What is the nth partial sum of the series 1 + 2 + 3 + 4 + ⋯ ?
What is the nth partial sum of the series 1 + 2 + 3 + 4 + ⋯ ?
- n(n+1)
- n(n+1)/2
- n(n-1)/2 (correct)
- n^2
As n goes to infinity, what happens to the nth partial sum of the series 1 + 2 + 3 + 4 + ⋯ ?
As n goes to infinity, what happens to the nth partial sum of the series 1 + 2 + 3 + 4 + ⋯ ?
- It approaches a finite value
- It oscillates
- It approaches 0
- It approaches infinity (correct)
What does the formula 1 + 2 + 3 + 4 + ⋯ = -1/12 mean?
What does the formula 1 + 2 + 3 + 4 + ⋯ = -1/12 mean?
Signup and view all the answers
What is the value of the series 1 + 2 + 3 + 4 + ⋯ according to zeta function regularization and Ramanujan summation?
What is the value of the series 1 + 2 + 3 + 4 + ⋯ according to zeta function regularization and Ramanujan summation?
Signup and view all the answers
