pvainfin a1 k-1 a1 k-2 a1 kinfin 1 a 1

Question

PVA_∞ = A(1 + k)^-1 +  A(1 + k)^-2+..... + A(1 + k^{)∞ + 1}+ A (1 + k)_∞

Multiplying both the sides of Eq (a7) by (1+k) provides:

PVA_∞  = (1 +k) = A(1 +k) +A (1 +k)^-1 +......A (1 +k)^{-∞ + 2} +A(1 + k)^{-∞ +1}

Subtracting Eq (a7) from eq (a8) provides:

PVA_∞ k = A [1 - (1 + k)^∞ ]

 As (1 + k)^-∞  → o eq.(a8) turns into:

PVA_∞ k = A

 ⇒ PVA_∞ = A/k