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avatar+1763 

Let $r$ be the positive real solution to $x^3 + \frac{2}{5} x - 1 = x^3 - 3x + 7.$ Find the exact numerical value of
\[r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb.\]

 Jan 10, 2024
 #1
avatar+128448 
+1

Simplify as

 

(2/5)x - 1 = -3x + 7

 

2x - 5  = -15x + 35

 

17x  = 40

 

x = 40 / 17  = r

 

Since r >  1, this  series does not converge to any value

 

 

cool cool cool

 Jan 10, 2024

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