List questions from induction

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When do you need to prove more than 1 base case in the Fibonacci problem?

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In proof by induction, what happens if P(n) is false for a specific case or the base cases are false? Can we still deduce meaningful conclusions?

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Prove by induction: $1(1!)+\cdots + n\cdot n!$ = (n+1)! - 1

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Structural Induction help

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Induction assuming n-1

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Proof by induction that $a_0 = 1, a_1 = 1, a_n=2a_{n-1} + 3a_{n-2}$ satisfies $a_n = \frac12 (3^n) + \frac12 (-1)^n$

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Induction Proof: Round Robin

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prove that the sum to n terms of the sequence is $n(n+1)/2(2n+1)$

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Induction -- n to n+1

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proof by induction - explanation on it

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Induction for recurrence

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Prove by induction that $n < 2^n$ for all $n \ge 1$

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Sum of the first $n$ numbers that is neither divisible by 2 nor 3.

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Why is the invariant of the following state machine (2 mod 5) OR (3 mod 5)?

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List Question

prove a recursive function by induction

When do you need to prove more than 1 base case in the Fibonacci problem?

In proof by induction, what happens if P(n) is false for a specific case or the base cases are false? Can we still deduce meaningful conclusions?

Prove by induction: $1(1!)+\cdots + n\cdot n!$ = (n+1)! - 1

Structural Induction help

Induction assuming n-1

Proof by induction that $a_0 = 1, a_1 = 1, a_n=2a_{n-1} + 3a_{n-2}$ satisfies $a_n = \frac12 (3^n) + \frac12 (-1)^n$

Induction Proof: Round Robin

prove that the sum to n terms of the sequence is $n(n+1)/2(2n+1)$

Induction -- n to n+1

proof by induction - explanation on it

Induction for recurrence

Prove by induction that $n < 2^n$ for all $n \ge 1$

Sum of the first $n$ numbers that is neither divisible by 2 nor 3.

Why is the invariant of the following state machine (2 mod 5) OR (3 mod 5)?

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