zeion
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Homework Statement
Show that the statement holds for all positive integers n
2^0 + 2^1 + 2^2 + 2^3 + ... + 2^{n-1} = 2^n - 1
Homework Equations
The Attempt at a Solution
Assume:
2^0 + 2^1 + 2^2 + 2^3 + ... + 2^{k-1} = 2^k - 1 is true.
Then:
2^{k+1}-1 = 2^k(2) - 1 = 2(2^0 + 2^1 + 2^2 + 2^3 + ... + 2^{k-1})
Not sure what to do next :/
Show that:
2^k(2) - 1 = 2(2^0 + 2^1 + 2^2 + 2^3 + ... + 2^{k-1}) is true