Answer:
Step-by-step explanation:
Given the following geometric progression; 1/2 + 1/10 + ( 1/50) + (1/250 ) + ... + (1/31,250),the sum of the arithmetic geometric progression is expressed using the formula below;
Sn = a(1-rⁿ)/1-r for r less than 1
r is the common ratio
n is the number of terms
a is the first term of the series
In between the mid-line ellipsis there are 2 more terms, making the total number of terms n to be 7]
common ratio = (1/10)/(1/2) = (1/50)/(1/10) = (1/250)/(1/50) = 1/5
a = 1/2
Substituting the given values into the equation above
S7 = 1/2{1 - (1/5)⁷}/1 - 1/5
S7 = 1/2(1- 1/78125)/(4/5)
S7 = 1/2 (78124/78125)/(4/5)
S7 = 78124/156,250 * 5/4
S7 = 390,620/625000
S7 = 39062/62,500
Hence the geometric sum is 39062/62,500
