Raymond B. answered • 05/23/21
Tutor
5
(2)
Math, microeconomics or criminal justice
Sum = a/(1-r) where r is the common ratio and a is the first term
a=1 and r=-1/5
S = 1(1--1/5) = 1/(1+1/5) = 1/(6/5) = 5/6 0.8333....
the sum = 5/6
partial sums of 2 and more terms
S2 = 4/5 = 0.8
S3 = 4/5+ 1/25 = 21/25 = 0.84
S4 = 21/25 - 1/125 = 104/125 = 0.832
S5 = 104/125 + 1/625 = 521/625 = 0.8336
You can see the partial sums approaching 0.8333.... = 5/6
the partial sums alternative a little above and a little below 0.8333...
