document.write( "Question 1092410: Please help... Thank you.
\n" ); document.write( "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
\n" ); document.write( "I got U2=1/3, U3=1/9, U4=1/27, but not sure about converge. \n" ); document.write( "

Algebra.Com's Answer #707016 by Boreal(15235) $\"\"$ $\"About$

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The ratio of each term to the prior is 1/3.
\n" ); document.write( "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.
\n" ); document.write( "partial sums are (108/243) and 36/243, and 4/243. This will converge to 0.
\n" ); document.write( "The ratio a/1-r is 1/3/1-(1/3)=(1/3)/(2/3)=(1/2).
\n" ); document.write( "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). \n" ); document.write( "

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