07%20-%20Sequences%20and%20Series

07%20-%20Sequences%20and%20Series - 07 SEQUENCES AND SERIES...

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07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) ( 1 ) If x = = 0 n n a , y = = 0 n n b , z = = 0 n n c , where a, b, c are in A.P. and l a l < 1, l b l < 1, l c l < 1, then x, y, z are in ( a ) G.P. ( b ) A.P. ( c ) Arithmetic-Geometric Progression ( d ) H.P. [ AIEEE 2005 ] ( 2 ) The sum of the series 1 + ! 2 4 1 + ! 4 6 1 1 + ! 6 4 6 1 + ……… ad inf. is ( a ) e 1 e - ( b ) e 1 e + ( c ) e 2 1 e - ( d ) e 2 1 e + [ AIEEE 2005 ] ( 3 ) If S n = = n 0 r n r C 1 and t n = = n 0 r n r C r , then n n S t = ( a ) n 2 1 ( b ) n 2 1 - 1 ( c ) n - 1 ( d ) 2 1 n 2 - [ AIEEE 2004 ] ( 4 ) Let T r be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers m, n, m n, T m = n 1 and T n = m 1 , then ( a ) 0 ( b ) 1 ( c ) mn 1 ( d ) m 1 + n 1 [ AIEEE 2004 ] ( 5 ) The sum of the first n terms of he series 1 2 + 2 2 2 + 3 2 + 2 4 2 + 5 2 + 2 6 2 + ….. is 2 ) 1 n ( n 2 + when n is even. When n is odd, the sum is ) 1 n ( n 3 + ) 1 n ( n 2 + ) 1 n ( n 2 + ) 1 n ( n + [ AIEEE 2004 ] ( 6 ) The sum of the series is ..... ! 6 1 ! 4 1 ! 2 1 + + + 1 e 2 - ) 1 e ( 2 - 1 e 2 - 2 e 2 - [ AIEEE 2004 ]
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07 - SEQUENCES AND SERIES Page 2 ( Answers at he end of all questions ) ( 7 ) The sum of the series + ...... 4 3 1 3 2 1 2 1 1 - - is ( a ) log e 2 ( b ) 2log e 2 ( c ) log e 2 - 1 ( d ) log e e 4 [ AIEEE 2003 ] ( 8 ) If the sum of the roots of the quadratic equation ax 2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then b c , a b , c a are in ( a ) A. P. ( b ) G. P. ( c ) H. P. ( d ) A. G. P. [ AIEEE 2003 ]
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