a2 - Department of Mathematics and Statistics McGill...

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Unformatted text preview: Department of Mathematics and Statistics McGill University MATH 242 Assignment 2 Due in class, Wednesday October 7 Full credit can be obtained from correct answers to questions totalling 70. 1. (10 points) Let n N and let a 1 , a 2 , . . . , a n . Show that 1 + n X j =1 a j n Y j =1 (1 + a j ) . 2. (10 points) Show by induction that 1 2 3 4 5 6 . . . 2 n- 1 2 n 2 1 3 n + 1 for n = 1 , 2 , . . . 3. (10 points) Let ( a j,k ) ( j,k ) N N be a double indexed family of nonnegative real numbers. (i) Show that inf ( j,k ) N N a j,k inf j N inf k N a j,k . (ii) Show that inf ( j,k ) N N a j,k inf j N inf k N a j,k . (iii) Deduce that inf k N inf j N a j,k = inf j N inf k N a j,k . 4. (10 points) Let ( a j,k ) ( j,k ) N N be a double indexed family of real numbers with | a j,k | 1 for all j and k . Show by example that sup k N inf j N a j,k 6 = inf j N sup k N a j,k in general....
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This note was uploaded on 11/05/2009 for the course MATH MATH 242 taught by Professor Drury during the Fall '09 term at McGill.

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a2 - Department of Mathematics and Statistics McGill...

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