Question
How many terms of the series
12+4+4/3+4/9+..., are needed to yield a sum of 1459/81?
12+4+4/3+4/9+..., are needed to yield a sum of 1459/81?
Answers
Reiny
this is a GS where a=12 and r=1/3
so using the sum formula
12( 1 - (1/3)^n )/(1-1/3) = 1459/81
1 - (1/3)^n = 1459/1458
(1/3)^n = -1/1458
<b>no solution.</b>
proof: the sum of the infinite number of terms
= a/(1-r) = 12/(1-1/3) = 12(3/2) = 18
and 1459/81 > 18
so using the sum formula
12( 1 - (1/3)^n )/(1-1/3) = 1459/81
1 - (1/3)^n = 1459/1458
(1/3)^n = -1/1458
<b>no solution.</b>
proof: the sum of the infinite number of terms
= a/(1-r) = 12/(1-1/3) = 12(3/2) = 18
and 1459/81 > 18