document.write( "Question 248545: Find the sum 1+ 1/2+1/4+...+1/1024\r
\n" ); document.write( "\n" ); document.write( "an=1+(n-1) ^ -1/2 \n" ); document.write( "

Algebra.Com's Answer #181153 by edjones(8007) $\"\"$ $\"About$

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(1/2)/1=1/2
\n" ); document.write( "(1/4)/(1/2)=1/2
\n" ); document.write( "r=1/2 Geometric sequence.
\n" ); document.write( " $\"a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29\"$
\n" ); document.write( "(1/2)^(n-1)=1/1024
\n" ); document.write( "log[1/2]((1/2)^n-1)=log[1/2](1/1024) Finding n
\n" ); document.write( "n-1=10
\n" ); document.write( "n=11
\n" ); document.write( " $\"S%5B11%5D=a%5B1%5D%28%281-r%5En%29%2F%281-r%29%29\"$ Sum of a finite geometric sequence.
\n" ); document.write( "= $\"1%28%281-%281%2F2%29%5E11%29%2F%281-%281%2F2%29%29%29\"$
\n" ); document.write( "=.9995/.5
\n" ); document.write( "=1.999... the sum \n" ); document.write( "

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