Convergence of Dynamic Programming

• Why does this converge?
• Infinite sum of discount coefficients
  • Σ _x=1,...,∞ γ^x, 0 < γ < 1
  • Integral test for convergence: If we rewrite the sum as an integral, and the integral converges, then the sum converges
  • ∫ _x=1,...,∞ γ^x, 0 < γ < 1
  • Antiderivative: γ ^x / ln γ
  • Calculate limit as x goes to ∞