document.write( "Question 1069243: Find the range of values of x for which the infinite series 1 +
\n" ); document.write( "lnx/2 +(lnx)^2/(2^2) + (lnx)^3/(2^3) + (lnx)^4/(2^4)+... converges. Find the sum to infinity when x=e^(1/2). \n" ); document.write( "

Algebra.Com's Answer #684446 by trsomas23@gmail.com(17) $\"\"$ $\"About$

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It is an infinite geometric series with common ratio
\n" ); document.write( "r = $\"ln%28x%29%2F2\"$
\n" ); document.write( "The series converges if
\n" ); document.write( "|r| < 1
\n" ); document.write( " $\"ln%28x%29%2F2\"$ < 1
\n" ); document.write( "ln(x) < 2
\n" ); document.write( "x < $\"e%5E2\"$
\n" ); document.write( "Sum of series = $\"a%2F%281-r%29\"$
\n" ); document.write( "= $\"1%2F%281-ln%28x%29%2F2%29\"$
\n" ); document.write( "When x = $\"e%5E%281%2F2%29\"$ , then the sum of the series
\n" ); document.write( "= $\"1%2F%281-1%2F4%29\"$
\n" ); document.write( "= $\"1%2F%283%2F4%29\"$
\n" ); document.write( "= $\"4%2F3\"$ \n" ); document.write( "

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