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1)Proof of Euler's formula, V-E+F=2, with induction on F (number of faces). Induction proof of the same formula using number edges as induction variable has a much simpler base case.

2)Backward induction proof of generalized AM-GM inequality.

3)Proof of Heine-Borel theorem using Transfinite Topological induction.

ADDED LATER: The Maximum Sum Contiguous Subsequence Problem is another interesting one. The problem of determining such a sequence becomes very cumbersome with naive inductionon the length of the sequence. But, strengthening the induction hypothesis with suffix sequence makes the problem almost trivial to solve.

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1)Proof of Euler's formula, V-E+F=2, with induction on F (number of faces). Induction proof of the same formula using number edges as induction variable has a much simpler base case.

2)Backward induction proof of generalized AM-GM inequality.

3)Proof of Heine-Borel theorem using Transfinite Topological induction.

ADDED LATER: The Maximum Sum Contiguous Subsequence Problem is another interesting one. The problem of determining such a sequence becomes very cumbersome with naive induction on the length of the sequence. But, strengthening the induction hypothesis with suffix sequence makes the problem almost trivial to solve.

4 added 319 characters in body

1)Proof of Euler's formula, V-E+F=2, with induction on F (number of faces). Induction proof of the same formula using number edges as induction variable has a much simpler base case.

2)Backward induction proof of generalized AM-GM inequality.

3)Proof of Heine-Borel theorem using Transfinite induction.

ADDED LATER: The Maximum Sum Contiguous Subsequence Problem is another interesting one. The problem of determining such a sequence becomes very cumbersome with naive induction on the length of the sequence. But, strengthening the induction hypothesis with suffix sequence makes the problem almost trivial to solve.

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