document.write( "Question 1074844: Good morning maam/sir..kindly help me with the following:
\n" ); document.write( "Derive the formula representing the following sums:
\n" ); document.write( "1. (1/1.2) + (1/2.3) + (1/3.4) +...+ 1/n.(n+1)
\n" ); document.write( "2. (n+1)^2 + (n+2)^2 + (n+3)^2 +...+ (2n)^2
\n" ); document.write( "3. 1.n + 2(n-1) + 3(n-2) +...+ (n-2).2 + n.1 \n" ); document.write( "

Algebra.Com's Answer #689520 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Good morning maam/sir..kindly help me with the following:
\n" ); document.write( "Derive the formula representing the following sums:\r
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document.write( "1. (1/1.2) + (1/2.3) + (1/3.4) +...+ 1/n.(n+1)\r\n" );
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document.write( "2. (n+1)^2 + (n+2)^2 + (n+3)^2 +...+ (2n)^2\r\n" );
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document.write( "3. 1.n + 2(n-1) + 3(n-2) +...+ (n-2).2 + n.1\r\n" );
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document.write( "1.   = .\r\n" );
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document.write( "    See the lesson Mathematical induction for sequences other than arithmetic or geometric, Problem 4.\r\n" );
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document.write( "2.      = \r\n" );
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document.write( "    =  - \r\n" );
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document.write( "    = .\r\n" );
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document.write( "    It uses the basic formula   = .\r\n" );
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document.write( "    See the lesson Mathematical induction for sequences other than arithmetic or geometric, Problem 1.\r\n" );
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\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
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document.write( "For #3 I will not derive the final formula.\r\n" );
document.write( "I will simply explain you how to get it.\r\n" );
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document.write( "     +        +      = \r\n" );
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document.write( "     +    +    = \r\n" );
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document.write( "     +    +    = \r\n" );
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document.write( ". . . . . . . . . . . . . . . . . . . . . . . \r\n" );
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document.write( " +     +        = \r\n" );
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document.write( "     +       +        = \r\n" );
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document.write( "------------------------------------------- Add all equations, both the left sides and the right sides.   You will get\r\n" );
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document.write( "  +       +  = ,\r\n" );
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document.write( "where\r\n" );
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document.write( " is exactly your sum under the question, and\r\n" );
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document.write( " = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point I will stop my explanations.\r
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\n" ); document.write( "\n" ); document.write( "If you have a necessary background/training/education in Math, then these tips are enough and you will be able to complete it on your own.\r
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\n" ); document.write( "\n" ); document.write( "If you do not have it, then any further explanations are useless.\r
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\n" ); document.write( "By the way, your formula in #3 is not exactly correct.
\n" ); document.write( "The correct formula is \r
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\n" ); document.write( "\n" ); document.write( "3. 1.n + 2(n-1) + 3(n-2) +...+ (n-1).2 + n.1\r
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document.write( "     Honestly, I don't like very much to work for those who is not able to write his/her formulas \r\n" );
document.write( "     (and, in general, the condition to the problem) correctly.\r\n" );
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