Asked by Sangita
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
Answered by
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.