Solution:
Given:
Sp = 1 + rp + r2p + … ∞
By using the formula,
S∞ = a/(1 – r)
Where, a = 1, r = rp
So,
Sp = 1 / (1 – rp)
Similarly, sp = 1 – rp + r2p – … ∞
By using the formula,
S∞ = a/(1 – r)
Where, a = 1, r = -rp
So,
Sp = 1 / (1 – (-rp))
= 1 / (1 + rp)
Now, Sp + sp = [1 / (1 – rp)] + [1 / (1 + rp)]
2S2p = [(1 – rp) + (1 + rp)] / (1 – r2p)
= 2 /(1 – r2p)
∴ 2S2p = Sp + Sp