Proof by Induction (AQA A-Level Further Maths): Flashcards

Prove statements true for all natural numbers

Positive integers: $1, 2, 3, 4, ...$

Base case: prove true for $n = 1$

Assume for $n=k$, prove for $n=k+1$

State true for all $n \in \mathbb{N}$ by induction

Assumption that statement is true for $n = k$

Three: base case, inductive step, conclusion

$\sum_{r=1}^{k} + (k+1)$th term

Separate assumed divisible part, show as multiple

Multiple of divisor, e.g. $3A$ for integer $A$