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 \[r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb.\]
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
+1859 
