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Compute
\(1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + \dotsb.\)

 Apr 16, 2024
 #1
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0

This is a geometric series with first term 1 and common ratio 61​. Since the absolute value of the common ratio is less than 1, the

series converges.

 

We can compute the sum of a geometric series using the following formula:

 

S=1−ra1​​

 

where a1​ is the first term and r is the common ratio.

 

In this case, we have a1​=1 and r=61​, so the sum of the series is:

 

S = 1/(1 - 1/6) = 1/(5/6) = 6/5.

 Apr 28, 2024

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