DE3619 DISTANCE EDUCATION B.Sc. (Mathematics) DEGREE EXAMINATION, MAY 2012. CLASSICAL ALGEBRA Time : Three hoursMaximum : 100 marks Answer any FIVE questions. All questions carry equal marks. (5 20 = 100) 1.(a)Examinetheconvergenceoftheseries ( )L L ++ + + +knk k knx x x1 2 5 3 111 2(10) (b)ProvethatL ++++ 9 747 535 323 11isdivergent. (10) 2.(a)Test for convergence of the series =++031 21nnn.(10) (b)Examinetheconvergenceoftheseries ( )( ) ( )+ + +nnn n n n L 2 1.(10) 3.(a)Findtheco-efficientof nx intheexpansionof xex z23 2 1 +.(10) (b)Show thatL + ||

\|+ + ||

\|+ + ||

\|+ + =3 24171614151414131211 2 log(10) 13 DE3619 2 4.(a)Sum the seriesL ++ + +++ ++++! 43 3 3 1! 33 3 1! 23 113 2 2 to (10) (b)Sum the series to infinity L + ++32 25 1627 21 1524 1621 151615(10) 5.(a)If , , ,be the roots of the biquadratic equation 02 3 4= + + + + s rx qx px x , find(i) 2(ii) 2 (iii) 2 2 (iv) 3 (v) 4 .(10) (b)Find 5 5 51 1 1 + + where , , aretherootsof the equation0 1 3 22 3= + x x x .(10) 6.(a)Solve the equation0 6 2 5 42 3 4= + + + x x x x .(10) (b)Solve the equation0 8 36 18 812 3= + x x x .(10) 7.(a)Prove that 1 2121 26543211 21+