Mathematics · Infinite Series
Let ∑ an be an infinite series with an > 0. Which of the following statements is FALSE?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1If ∑ an is convergent and bn = (a1 + a2 + ... + an)/n for all n ∈ &mathbb{N}, then ∑ bn is always convergent.✓
- 2If ∑ an is convergent, then ∑ an2 is always convergent.
- 3If ∑ an is convergent, then ∑ √(an · an+1) is always convergent.
- 4If ∑ an is convergent, then ∑ √an may not be convergent.
Correct answer
If ∑ an is convergent and bn = (a1 + a2 + ... + an)/n for all n ∈ &mathbb{N}, then ∑ bn is always convergent.
Download Single Question PDF
Save this question and verified answer as a clean study sheet with live clickable link.
👥
Share with Friends & Study Groups
Challenge your peer aspirants on WhatsApp or Telegram to solve this question!
Online Test Series
Start Free Mock Test →Preparing for Mathematics?
Practice full-length mock tests with real exam timers, instant score analysis, and all-India ranking.
Chapter Practice
Practice Infinite Series MCQs →Want more practice questions on Infinite Series?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Infinite Series