I am to prove the following statement using mathematical induction for all positive integers:
1−2+22−23+⋯+(−1)n2n=2n⋅21⋅(−1)n+13.
However, for the basis step, I am getting −2 for the left side and −1 for the right side, which are obviously not equal. The assignment indicates that the statement is true though, so I am missing something or could this be a typo in the statement?
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