# Find the number of different sums that can be obtained by using one,some or all of the numbers in the set{1,2,4,8}.Then, how about from {#2^0,2^1,2^2,..,2^n#}?

We can prove this result by induction...

Base case

Induction step

Conclusion

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For the set {1, 2, 4, 8}, the number of different sums that can be obtained by using one, some, or all of the numbers is 15.

For the set {2^0, 2^1, 2^2, ..., 2^n}, where n is a non-negative integer, the number of different sums that can be obtained by using one, some, or all of the numbers is (2^{n+1} - 1).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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