document.write( "Question 864619: Find the sum of the series: 12 - 6 + 3 - 3/2 + ... \n" ); document.write( "
Algebra.Com's Answer #521259 by richwmiller(17219)\"\" \"About 
You can put this solution on YOUR website!
S=t*(1 - r^n)/(1 - r)
\n" ); document.write( "where r=-1/3 t=12
\n" ); document.write( "S=12*(1 - 1/3^n)/(1 - (-1/3))
\n" ); document.write( "S = 9(1-3^(-n))
\n" ); document.write( "An infinite geometric series converges if its common ratio r satisfies –1 < r < 1.
\n" ); document.write( "Our ratio is -1/3 so it converges.
\n" ); document.write( "lim_(n->infinity) 9 (1-3^(-n)) = 9\r
\n" ); document.write( "\n" ); document.write( "S = 9 (1-3^(-n))
\n" ); document.write( "let's try a few numbers and see what happens
\n" ); document.write( "S=12*(1 - 1/3^10)/(1 - (-1/3)),
\n" ); document.write( "T=12*(1 - 1/3^20)/(1 - (-1/3)),
\n" ); document.write( "U=12*(1 - 1/3^30)/(1 - (-1/3))
\n" ); document.write( "V=12*(1 - 1/3^100)/(1 - (-1/3))
\n" ); document.write( "as expected
\n" ); document.write( "S=8.9998, T=9.0000, U=9.0000, V=9.0000
\n" ); document.write( "even as early as n=10 it is almost 9\r
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