Series and Summation

Question

Find the sum of the geometric sequence.  1, one divided by two, one divided by four, one divided by eight, one divided by sixteen

Answer 1

Geometric sequence : 1, 1/2, 1/4, 1/8, 1/16.

first term a1 = 1 and common ratio r = a2 / a1 = (1/2)/1 = 1/2 and n = 5

Calculate the Find the sum of the geometric sequence by using formula : Sn = [a1(1-r^n)]/(1-r), r ≠ 1.

Sn = [(1)*(1-(1/2)^5)]/(1-(1/2))

Sn = [(1-1/32))]/(1/2)

Sn = [(32-1)/32))]/(1/2)

Sn =31/16.