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a) Use notation to write the following sum in a compact form: ... - n+2(n-1)+3(n − 2) + + (n − 2)3 + (n − 1)2 + n - - b) Use mathematical induction to show that for any nЄ N, - - • n+2(n − 1) + 3(n − 2) + ··· + (n − 2)3 + (n − 1)2 + n = - - n(n + 1)(n+2) 6 (Hint: When you want to go from the hypothesis p(n) to the conclusion p(n+1), show that you just need to prove that LHS(n + 1) − LHS(n) = RHS(n + 1) − RHS(n), and use this trick to simplify your calculations) -

a) Use notation to write the following sum in a compact form: ... - n+2(n-1)+3(n − 2) + + (n − 2)3 + (n − 1)2 + n - - b) Use mathematical induction to show that for any nЄ N, - - • n+2(n − 1) + 3(n − 2) + ··· + (n − 2)3 + (n − 1)2 + n = - - n(n + 1)(n+2) 6 (Hint: When you want to go from the hypothesis p(n) to the conclusion p(n+1), show that you just need to prove that LHS(n + 1) − LHS(n) = RHS(n + 1) − RHS(n), and use this trick to simplify your calculations) -

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 42E
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a) Use notation to write the following sum in a compact form: ... - n+2(n-1)+3(n − 2) + + (n − 2)3 + (n − 1)2 + n - - b) Use mathematical induction to show that for any nЄ N, - - • n+2(n − 1) + 3(n − 2) + ··· + (n − 2)3 + (n − 1)2 + n = - - n(n + 1)(n+2) 6 (Hint: When you want to go from the hypothesis p(n) to the conclusion p(n+1), show that you just need to prove that LHS(n + 1) − LHS(n) = RHS(n + 1) − RHS(n), and use this trick to simplify your calculations) -
Transcribed Image Text:a) Use notation to write the following sum in a compact form: ... - n+2(n-1)+3(n − 2) + + (n − 2)3 + (n − 1)2 + n - - b) Use mathematical induction to show that for any nЄ N, - - • n+2(n − 1) + 3(n − 2) + ··· + (n − 2)3 + (n − 1)2 + n = - - n(n + 1)(n+2) 6 (Hint: When you want to go from the hypothesis p(n) to the conclusion p(n+1), show that you just need to prove that LHS(n + 1) − LHS(n) = RHS(n + 1) − RHS(n), and use this trick to simplify your calculations) -
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