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If b/7 + (b^2)/(7^2) + (b^3)/(7^3) + (b^4)/(7^4) ...  =  7

 

What is b?

 May 23, 2022
 #1
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By geometric series, b = 50/7.

 May 23, 2022
 #2
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Using the sum of G.S. formula, we have 

\(\dfrac{\dfrac b7}{1 - \dfrac b7} = 7\\ \dfrac b7 = 7 - b\\ \dfrac {8b}7 = 7\\ b = \dfrac{49}8\)

 May 23, 2022

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