calculus-1-asignment-2.pdf - Jacobs University Bremen Prof...

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Jacobs University Bremen Fall Semester 2017 Prof. Dr. T. Preusser Calculus I Assignment Sheet 2. Due: Sep 18, 2017 Problem 4 [10 Points]: Prove the following formula by induction: For any n 2 N we have 1 + 4 + 9 + 16 + · · · + n 2 = 1 6 n ( n + 1)(2 n + 1) . Note: Instead of 1 + 4 + 9 + 16 + · · · + n 2 we can also write P n k =1 k 2 , so you have to show by induction that P n k =1 k 2 = 1 6 n ( n + 1)(2 n + 1). Problem 5 [10 Points]: We define a relation by the following: For x, y 2 Z we say that x y if and only if x - y is divisible by 3. Check whether this relation is an equivalence relation, i.e. whether it is reflexive, symmetric, and
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  • Fall '17
  • Tobias Pressuer
  • Transitive relation, Jacobs University Bremen

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