# hw1 - to move all the disks from tower A to tower B while...

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University of Engineering and Technology Lahore Department of Electrical Engineering Calculus I Problem Set #1 Due date: November 9, 2010 Reading Read Ch1 of textbook. We will not cover it in class, but expect that you have learnt this material in your F.Sc./A-levels. Appendix A.1 and Section 2.1 of textbook 1. Prove the following formulas by induction (a) 1 2 + ··· n 2 = n ( n +1)(2 n +1) 6 (b) 1 3 + ··· + n 3 = (1 + ··· + n ) 2 2. Find a formula for (a) n i =1 (2 i - 1) (b) n i =1 (2 i - 1) 2 3. Find an error in the inductive argument given in the class proving the fact that all the students have the same birthdays. 4. There is a puzzle consisting of three towers A , B and C , with N concentric disks of diﬀerent sizes. Initially we have all N disks stacked in decreasing size on the tower A , such that the largest disk is at the bottom and the smallest disk is on the top. We have
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Unformatted text preview: to move all the disks from tower A to tower B while observing the following rules: (i) one disk can be shifted at a time. (ii) no disk may be placed on top of a smaller one. For example if you want to move 3 disks then you should move top disk from tower A to B move top disk from tower A to C move top disk from tower B to C move top disk from tower A to B move top disk from tower C to A move top disk from tower C to B move top disk from tower A to B Prove that the entire stack of n rings can be moved onto tower C in 2 n-1 moves and that this cannot be done in fewer than 2 n-1 moves. 5. Exercise 2.1 (a) 2 (b) 4 (c) 17 1...
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## This note was uploaded on 01/10/2011 for the course EE 100 taught by Professor Razasuleman during the Spring '10 term at University of Engineering & Technology.

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