Find the sum of the geometric series 1 + 0.8 + 0.8^2 + 0.8^3 + ... + 0.8^{19}

S20 ≈ 4.942

Step-by-step explanation:

Sum of a geometric series is expressed as Sn = a (1-rⁿ) / 1-r if r<1

a is the first term

r is the common ratio

n is the number of terms

Given the geometric series

1 + 0.8 + 0.8^2 + 0.8^3 + ... + 0.8^{19}

Given a = 1,

r = 0.8/1 = 0.8²/0.8 = 0.8

n = 20 (The total number of terms in the series is 20)

Substituting this values in the formula above.

S20 = 1 (1-0.8^20) / 1-0.8

S20 = 1-0.01153/0.2

S20 = 0.9885/0.2

S20 ≈ 4.942