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(1) Use induction to prove 1(1!) + 2(2!) + 3(3!) + - - - -|- n(n!) = (n -|- 1)! 1 for every positive integer n. (This part is a stepping stone for...

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Im stuck on part (2), especially proving uniqueness.

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(1) Use induction to prove 1(1!) + 2(2!) + 3(3!) + - - - -|- n(n!) = (n -|- 1)! — 1 for every positive integer n. (This
part is a stepping stone for the next.)
(2) Prove that each positive integer n has a unique representation in the form n=a111+a22l+a33!+---+att! for some positive integer t and some integers a1, a2, . . . ,at where at % 0 and 0 g az- g i for l g 2' g t. (For
instance, 61 = 1! + 0 - 2! -|- 2 - 3! -|- 2 - 4!. Strong induction is useful for at least one part of this proof.)

Top Answer

You have to use strong induction to set up a proof. Your first step is the same as with any strong induction proof, you need... View the full answer

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