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# halp!

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Find the value of  given that
b/7+b^2/7^2+b^3/7^3.....=7

Jul 1, 2022

#1
+2275
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The common ratio of the series is $$b \over 7$$, and the starting term is $$b \over 7$$, so we have the equation: $$\large{{{b \over 7} \over 1 - {b \over 7}} = 7}$$

Multiplying the entire equation by $$1 - {b \over 7}$$ gives us $${b \over 7} = 7(1 - {b \over 7})$$, which simplifies to $${b \over 7} = 7 - b$$

Multiplying the entire equation by 7 gives us $$b = 49 - 7b$$, meaning $$b = \color{brown}\boxed{49 \over 8}$$

Jul 1, 2022