document.write( "Question 1175119: The series v + v^2 + v^3 + . . . has a limiting sum w.
\n" ); document.write( "a. Write w in terms of v.\r
\n" ); document.write( "\n" ); document.write( "b. Find v in terms of w.\r
\n" ); document.write( "\n" ); document.write( "c. Hence find the limiting sum of the series w − w^2 + w^3 − . . . , assuming that ∣w∣ < 1.\r
\n" ); document.write( "\n" ); document.write( "d. Test your results with v = 1/3
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Algebra.Com's Answer #800820 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
The series v + v^2 + v^3 + . . . has a limiting sum w.
\n" ); document.write( "a. Write w in terms of v.
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document.write( "\"S%5Binfinity%5D=a%5B1%5D%2F%281-r%29\"\r\n" );
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document.write( "\"w=v%2F%281-v%29\"\r\n" );
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b. Find v in terms of w.
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document.write( "\r\n" );
document.write( "\"w=v%2F%281-v%29\"\r\n" );
document.write( "\"w%281-v%29=v\"\r\n" );
document.write( "\"w-wv=v\"\r\n" );
document.write( "\"w=wv%2Bv\"\r\n" );
document.write( "\"w=v%28w%2B1%29\"\r\n" );
document.write( "\"w%2F%28w%2B1%29=v\"\r\n" );
document.write( "\"v=w%2F%28w%2B1%29\"\r\n" );
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\n" ); document.write( "c. Hence find the limiting sum of the series w − w^2 + w^3 − . . . , assuming
\n" ); document.write( "that ∣w∣ < 1.
\r\n" );
document.write( "\"S%5Binfinity%5D=a%5B1%5D%2F%281-r%29=w%2F%281-%28-w%29%29=w%2F%281%2Bw%29\"\r\n" );
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d. Test your results with v = 1/3
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document.write( "\"w=v%2F%281-v%29\"\r\n" );
document.write( "\"w=%281%2F3%29%2F%281-1%2F3%29\"\r\n" );
document.write( "\"w=%281%2F3%29%2F%282%2F3%29\"\r\n" );
document.write( "\"w=%281%2F3%29%2A%283%2F2%29\"\r\n" );
document.write( "\"w=%281%2Fcross%283%29%29%2A%28cross%283%29%2F2%29\"\r\n" );
document.write( "\"w=1%2F2\"\r\n" );
document.write( "------------------------------------------------\r\n" );
document.write( "\"v=w%2F%28w%2B1%29\"\r\n" );
document.write( "\"1%2F3=%281%2F2%29%2F%28%281%2F2%29%2B1%29\"\r\n" );
document.write( "\"1%2F3=%281%2F2%29%2F%283%2F2%29\"\r\n" );
document.write( "\"1%2F3=%281%2F2%29%2A%282%2F3%29\"\r\n" );
document.write( "\"1%2F3=%281%2Fcross%282%29%29%2A%28cross%282%29%2F3%29\"\r\n" );
document.write( "\"1%2F3=1%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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