Proof by Induction (Edexcel A-Level Further Mathematics): Flashcards

Summation of series, divisibility, matrix products

Base case - verify formula for $n=1$ or starting value

Assume formula holds for $n=k$

Prove formula holds for $n=k+1$

$\frac{n(n+1)(2n+1)}{6}$

$f(k+1) = f(k) + \text{(some multiple of } k\text{)}$

$km$ for some integer $m$

Failing to clearly define it

Errors simplifying expressions (powers, coefficients)

Misapplying initial conditions