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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.

1)Proof of Euler's formula, V-E+F=2, with induction on F (number of faces).

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

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

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.

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.

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.

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.