Question

Find the sum of the geometric series 1+.8+.8^2+.8^3+...+.8^19

Answer 1

Sum is about 4.9423

Explanation:

We want the sum: 1+.8+.8^2+.8^3+...+.8^19

Common ratio = r = 0.8

First term : a_1 = 1

20 terms here.

nth term : a_n = a_1 * r^(n - 1)

a_n = 1 * (0.8)^(n - 1)

Sum of first 20 terms = S

S = a_1 * ( ( r^20) - 1) / ( r - 1)

S = 1 * ( (0.8^20) - 1 ) / (0.8 - 1)

S = [(0.8^20) - 1 ] / (-0.2)

S = -0.98847078495393153024‬ / (-0.2)

S = 4.94235