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3 Feb 2012 22:26:28 IST
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find the sum of the following series (a+b)+(a^2+ab+b^2)+(a^3+a^2b+ab^2+b^3)+........
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4 Feb 2012 12:33:22 IST
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 [  ]
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Aman Raghuvanshi
Studies at: JRS Tutorials,Dehradun
Contact: +917579083742 |
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4 Feb 2012 17:05:36 IST
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explain
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5 Feb 2012 20:10:48 IST
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the given series in g.pa+b,(a+b)^2,(a+b)^3.....
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6 Feb 2012 12:33:50 IST
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look at the coefficients of the cross terms
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7 Feb 2012 11:32:40 IST
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oops...sorry
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7 Feb 2012 11:43:57 IST
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Add n subtract th requird terms for making it gp. . .and then find th sum of gp and remaining terms
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11 Feb 2012 12:24:16 IST
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what is the next term?? a4 +a3b+a2b2+ ab3+b4 or, a4 +a3b+2a2b2+ ab3+b4 Pls specify!! |
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11 Feb 2012 23:59:16 IST
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;et x = (a+b) + (a^2 + ab + b^2) + (a^3 + a^2(b) + a(b^2) + b^3) ...... multiply both the sides by (a-b). x(a-b) = (a^2-b^2) + (a^3 - b^3) + (a^4 - b^) + ...... use GP. the question is prety easy :)
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mathematics is the food of my soul.
There are 3 types of people in the world. Those who can count and those who can't . :-)
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12 Feb 2012 00:00:17 IST
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a slight typo there. it is (a^4-b^4).. :) sorry.
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mathematics is the food of my soul.
There are 3 types of people in the world. Those who can count and those who can't . :-)
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12 Feb 2012 21:19:51 IST
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Just multiply and divide the expression by (a-b) and sum it. The expression will become S = [(a2-b2) + (a3-b3) + (a4-b4) +..........]/(a-b) ( Sum of infinite GP 1+a+a2+a3+...... = 1/(1-a) ----------- (Geometric Progressions formula) ) So a2+a3+a4+.... = a2/(1-a). So S = [ (a2+a3+....) - (b2+b3+.....) ] / (a-b) So S = [ a2/(1-a) - b2/(1-b) ] / (a-b) or S = (a+b-ab)/[(1-a)(1-b)]
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13 Feb 2012 23:42:31 IST
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I DONT KNOW I AM RIGHT OR WRONG LET A= (a+b)+ (a^2 +ab+b^2) +(a^3+a^2b+ab^2+b^3)+.......................... A= (a+a^2+a^3+................)+(b+b^2+b^3+........)+(ab+ (a^2b+ab^2)+(a^3.b+a^2.b^2+a.b^3)+........) A= (a+a^2+a^3+..............)+(b+b^2+b^3+.......)+(ab + ab.(a+b)+ ab.(a^2+ab+b^2)+..................... ) A= (a+a^2+a^3+............)+(b+b^2+b^3+......)+ab(1+ (a+b)+ (a^2+ab+b^2)+..........................) A= (a+a^2+a^3+.........)+(b+b^2+b^3+.....)+ab(1+A) A -ab.A=(a+a^2+a^3+...........)+(b+b^2+b^3+.................)+ab A(1-ab)=(a+a^2+a^3+...........)+(b+b^2+b^3+................)+ab as i know you are not fool you will never say that a and b are greater or equal to -1 or lesser or equal to -1 so A(1-ab)= a/(1-a)+ b/(1-b) +ab after this solve by yourself
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14 Feb 2012 00:29:31 IST
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a mistake in last 5th line it is 1 not -1
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