Prove by induction: "Every natural number n can be represented as a sum of powers of 2."

[Matthew Prey]

"Every natural number n can be represented as a sum of powers of 2."

Tip : 2^b ≤ n < 2^(b+1) for all b ∈ N.

 

[eipi45]

this boils down to every n can be expressed in binary

 

[Dr.Peterson]

"Every natural number n can be represented as a sum of powers of 2."

Tip : 2^b ≤ n < 2^(b+1) for all b ∈ N.

Please show some effort, as we ask:

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Have you thought about how induction might be applied?

The hint might be read as suggesting that you use induction on b, rather than on n. You will need to express what you want to prove in an appropriate way.

 

[lev888]

"Every natural number n can be represented as a sum of powers of 2."

Tip : 2^b ≤ n < 2^(b+1) for all b ∈ N.

If this is the exact problem statement then there is nothing to prove. 1 is a power of 2 and any number n is a sum of n 1s. I'm guessing they want distinct powers of 2.