Use strong induction to show that every positive integer, n, can be written as a sum...

Use strong induction to show that every positive integer, n, can be written as a sum of powers of two: 2⁰, 2¹, 2², 2³, .....

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FROM THE GIVEN DATA WE CAN SOLVE AS FOLLOWS

Colby Messinger answered 2 years ago

Use strong induction to show that every positive integer n can be written as a sum...

Use strong induction to show that every positive integer n can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 2^0 =1, 2^1 = 2, 2^2 = 4, and so on. [Hint: For the inductive step, separately consider the case where k + 1 is even and where it is odd. When it is even, note that (k + 1)/2 is an integer.]

Use induction to prove that for any positive integer n, 8^n - 3^n is a multiple...

Use induction to prove that for any positive integer n, 8^n - 3^n is a multiple of 5.

Use mathematical induction to prove that for every integer n >=2, if a set S has...

Use mathematical induction to prove that for every integer n >=2, if a set S has n elements, then the number of subsets of S with an even number of elements equals the number of subsets of S with an odd number of elements. pleases send all detail solution.

Prove or disprove that 3|(n 3 − n) for every positive integer n.

1a. Proof by induction: For every positive integer n, 1•3•5...(2n-1)=(2n)!/(2n•n!). Please explain what the exclamation mark...

1a. Proof by induction: For every positive integer n, 1•3•5...(2n-1)=(2n)!/(2n•n!). Please explain what the exclamation mark means. Thank you for your help! 1b. Proof by induction: For each integer n>=8, there are nonnegative integers a and b such that n=3a+5b

a. Use mathematical induction to prove that for any positive integer ?, 3 divide ?^3 +...

a. Use mathematical induction to prove that for any positive integer ?, 3 divide ?^3 + 2? (leaving no remainder). Hint: you may want to use the formula: (? + ?)^3= ?^3 + 3?^2 * b + 3??^2 + ?^3. b. Use strong induction to prove that any positive integer ? (? ≥ 2) can be written as a product of primes.

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Use strong induction to show that every positive integer, n, can be written as a sum...

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