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Find the sum of \(\frac{1}{7}+\frac{2}{7^2}+\frac{1}{7^3}+\frac{2}{7^4}+...\)

 Jun 16, 2023
 #1
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sumfor(n, 1, 10000, (1/7^(2*n - 1) + 2/(7^(2*n)))==3 / 16

 Jun 16, 2023
 #2
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The sum of the infinite series 1/7 + 2/7^2 + 1/7^3 + 2/7^4 + ... is 9/48.

This can be found using the formula for the sum of a geometric series:

S = a/(1-r)

where

a = first term in the series

r = common ratio

S = sum of the series

In this case,

a = 1/7

r = 2/7

S = ?

S = 1/7 / (1 - 2/7) = 9/48

Therefore, the sum of the infinite series is 9/48.

 Jun 16, 2023
 #3
avatar+33616 
+1

Like so:

 

 Jun 16, 2023
 #4
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Thank you all!

 Jun 20, 2023

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