Use the Ratio Test to determine whether the series is convergent or divergent. $\sum_{i=1}^{m} k e^{-k}$
Added by Victoria V.
Step 1
First, we apply the Ratio Test: $$\lim_{k\to\infty} \frac{(k+1)e^{-(k+1)}}{ke^{-k}} = \lim_{k\to\infty} \frac{k+1}{k} e^{-1} = e^{-1}$$ Since the limit is less than 1, the series converges by the Ratio Test. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Adi S and 61 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Sequences, Series, and Power Series
The Ratio and Root Tests
Use the Ratio Test to determine whether the series is convergent or divergent. $\sum_{i=1}^{\infty} \frac{1}{k !}$
Use the Ratio Test to determine whether the series is convergent or divergent. $ \displaystyle \sum_{k = 1}^{\infty} \frac {1}{k!} $
Infinite Sequences and Series
Absolute Convergence and the Ratio and Root Tests
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD