SOLUTION: Please help... Thank you. Determine whether the sequence converges or diverges. If it converge, give the limit. U 1=1 and U n+1=(Un)/(3) for n≥1 I got U2=1/3, U3=1/9, U4=1

Algebra ->  Sequences-and-series -> SOLUTION: Please help... Thank you. Determine whether the sequence converges or diverges. If it converge, give the limit. U 1=1 and U n+1=(Un)/(3) for n≥1 I got U2=1/3, U3=1/9, U4=1      Log On


   

Question 1092410: Please help... Thank you.
Determine whether the sequence converges or diverges. If it converge, give the limit. U 1=1 and U n+1=(Un)/(3) for n≥1
I got U2=1/3, U3=1/9, U4=1/27, but not sure about converge.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio of each term to the prior is 1/3.
Sequence is 1/3, 1/9, 1/27, 1/81, 1/243. As n increases, lim of 1/3^n =0. That helps but doesn't prove convergence.
partial sums are (108/243) and 36/243, and 4/243. This will converge to 0.
The ratio a/1-r is 1/3/1-(1/3)=(1/3)/(2/3)=(1/2).
The series itself converges to 0, and the sum of the series, if one starts at 1/3, converges to (1/2). If it started with 1, then it would converge to (3/2).