document.write( "Question 1085009: 
I need the answer for question (i) and (ii) both of them please:\r\n" );
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document.write( "(2) Let {an} and {bn} for n = 1,2,3,... .\r\n" );
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document.write( "(i) The sequence {an} satisfies the following relation:\r\n" );
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document.write( "                     \"1%2Fa%5Bn%2B1%5D-1%2Fa%5Bn%5D=2\".\r\n" );
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document.write( "Express the general term an in terms of n when a1 = \"1%2F6\"\r\n" );
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document.write( "(ii) The general term of {bn} is given by\r\n" );
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document.write( "                     \"b%5Bn%5D=sqrt%281%2Bn%5E2%29-n\"\r\n" );
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document.write( "                     Prove that \"b%5Bn%5D%3E=b%5Bn%2B1%5D\"
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Algebra.Com's Answer #699045 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Here's your second one:\r\n" );
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document.write( "(ii) The general term of {bn} is given by\r\n" );
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document.write( "        \"b%5Bn%5D=sqrt%281%2Bn%5E2%29-n\"\r\n" );
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document.write( "         Prove that \"b%5Bn%5D%3E=b%5Bn%2B1%5D\"\r\n" );
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document.write( "Assume that it is false for contradiction, that is we assume:\r\n" );
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document.write( "\"b%5Bn%5D%3Cb%5Bn%2B1%5D\"\r\n" );
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document.write( "\"sqrt%281%2Bn%5E2%29-n%3Csqrt%281%2B%28n%2B1%29%5E2%29-%28n%2B1%29\"\r\n" );
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document.write( "\"sqrt%281%2Bn%5E2%29-n%3Csqrt%281%2B%28n%2B1%29%5E2%29-n-1\"\r\n" );
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document.write( "\"sqrt%281%2Bn%5E2%29%3Csqrt%281%2Bn%5E2%2B2n%2B1%29-1\"\r\n" );
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document.write( "\"sqrt%281%2Bn%5E2%29%3Csqrt%28n%5E2%2B2n%2B2%29-1\"\r\n" );
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document.write( "\"sqrt%281%2Bn%5E2%29%2B1%3Csqrt%28n%5E2%2B2n%2B2%29\"\r\n" );
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document.write( "Since both sides are positive we can square both\r\n" );
document.write( "sides and retain the inequality <\r\n" );
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document.write( "\"%281%2Bn%5E2%29%2B2sqrt%281%2Bn%5E2%29%2B1%3Cn%5E2%2B2n%2B2\"\r\n" );
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document.write( "\"1%2Bn%5E2%2B2sqrt%281%2Bn%5E2%29%2B1%3Cn%5E2%2B2n%2B2\"\r\n" );
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document.write( "\"2%2Bn%5E2%2B2sqrt%281%2Bn%5E2%29%3Cn%5E2%2B2n%2B2\"\r\n" );
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document.write( "Isolate the radical term on the left:\r\n" );
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document.write( "\"2sqrt%281%2Bn%5E2%29%3C2n\"\r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( "\"sqrt%281%2Bn%5E2%29%3Cn\"\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "\"1%2Bn%5E2%3Cn%5E2\"\r\n" );
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document.write( "\"1%3C0\"\r\n" );
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document.write( "A contradiction, so the inequality is proved.\r\n" );
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document.write( "\"b%5Bn%5D%3E=b%5Bn%2B1%5D\"\r\n" );
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document.write( "Edwin
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