(2) (5 points) Use strong induction to show that every positive integer can be written as a sum of distinct powers of tw

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2 5 Points Use Strong Induction To Show That Every Positive Integer Can Be Written As A Sum Of Distinct Powers Of Tw 1 (26.46 KiB) Viewed 47 times

(2) (5 points) Use strong induction to show that every positive integer can be written as a sum of distinct powers of two (i.e., 20= 1,2¹ = 2, 22- 4,238,24 16,...). = - For example: 19 = 16+2+1=24+2¹+20 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.