Question
Determine whether the series is convergent or divergent. If it is convergent, find its sum.$ \displaystyle \sum_{n = 1}^{\infty} 3^{n + 1} 4^{-n} $
Step 1
To do this, we rewrite the series as follows: \[ \displaystyle \sum_{n = 1}^{\infty} 3^{n + 1} 4^{-n} = \displaystyle \sum_{n = 1}^{\infty} 3 \cdot \left(\frac{3}{4}\right)^n \] Show more…
Show all steps
Your feedback will help us improve your experience
J Hardin and 78 other Calculus 2 / BC 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
Determine whether the series is convergent or divergent. If it is convergent, find its sum. $\sum_{n=1}^{n} 3^{n+1} 4^{-n}$
Sequences, Series, and Power Series
Series
Determine whether the series is convergent or divergent. If it is convergent, find its sum. $$\sum_{n=1}^{\infty} \frac{1+2^{n}}{3^{n}}$$
SERIES
Determine whether the series is convergent or divergent. If it is convergent, find its sum. $$\sum_{n=1}^{\infty} \frac{1+3^{n}}{2^{n}}$$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD