Mathematical induction involving series (HSC SSCE Mathematics Extension 1): Flashcards

A method to prove statements for all natural numbers.

It verifies the statement for the first value, n=1.

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

The summation of a sequence of numbers.

Sum = n(n+1)/2.

Validate base case, assume, then prove for n=k+1.

S_n = n/2(2a + (n-1)d) where a is the first term.

1^2 + 2^2 + ... + n^2 = n(n+1)(2n+1)/6.

It helps form assumptions for induction proofs.

Base case, inductive step, conclusion for n ≥ 1.