Question 1137525
<font face="times" color="black" size="3">
We start with 5/4 as the first term
To get the next term, we multiply by 1/4
(5/4)*(1/4) = 5/16
and then multiply that term by 1/4 to get the third term
(5/16)*(1/4) = 5/64
and so on


a = 5/4 is the first term
r = 1/4 is the common ratio
Because r = 1/4 = 0.25 is between -1 and 1, this means the infinite geometric series does converge. In other words, that r value makes -1 < r < 1 true.


So we use the formula below to find the infinite sum S
{{{S = a/(1-r)}}}


{{{S = (5/4)/(1-1/4)}}}


{{{S = (5/4)/(4/4-1/4)}}}


{{{S = (5/4)/(3/4)}}}


{{{S = (5/4)*(4/3)}}}


{{{S = (5*4)/(4*3)}}}


{{{S = (5*highlight(4))/(highlight(4)*3)}}}


{{{S = (5*cross(4))/(cross(4)*3)}}}


{{{S = 5/3}}}


The geometric series converges to the sum of 5/3 = 1.6667</font>