Geometric series Evaluate the geometric series

Chapter 11, Problem 32E

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QUESTION:

19-34. Geometric series Evaluate the geometric series or state that it diverges.

\(\sum_{k=1}^{\infty} \frac{3^{k-1}}{4^{k+1}}\)

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QUESTION:

19-34. Geometric series Evaluate the geometric series or state that it diverges.

\(\sum_{k=1}^{\infty} \frac{3^{k-1}}{4^{k+1}}\)

ANSWER:

Problem 32E

Geometric series 
Evaluate the geometric series or state that it diverges.

Solution:
Step 1
The given series is :  
Taking
the series becomes :

     

     =

From this, we get

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