I know the principle of mathematical induction. The only thing that causes my confusion is that we suppose a statement is true for n=k then we prove the statement is also true for n=k+1 but how can we suppose n=k to be true? What if a statement is true for n=k+1 and is not true for n=k? Does k mean to be starting from 1 or 2 if in the base case we prove the statement to be valid for n=1? Please help me with this confusion.
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