Prove that \sum_{i=0}^{n} 2^{i} = 2^{n + 1} - 1 Use mathematical induction for this proof and discuss/explain each step.
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Let us prove that using mathematical induction.
For we have that the left side is and the right side is Therefore, for the equality is true.
Suppose that the equality is true for that is
Let us prove for
It follows that
We conclude that by principle of mathematical induction the statement is true for all natural numbers