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Geometric series Evaluate the geometric series
Chapter 11, Problem 22E(choose chapter or problem)
QUESTION:
19-34. Geometric series Evaluate the geometric series or state that it diverges.
\(\sum_{k=0}^{\infty} \frac{2^{k}}{7^{k}}\)
Questions & Answers
QUESTION:
19-34. Geometric series Evaluate the geometric series or state that it diverges.
\(\sum_{k=0}^{\infty} \frac{2^{k}}{7^{k}}\)
ANSWER:Problem 22E
Geometric series Evaluate the geometric series or state that it diverges.
Solution
Step 1
In this problem we have to evaluate the geometric series or we have to state that it diverges.
The sum of an infinite Geometric series is given by if .
We have
Here and
Hence the sum ofis