Induction

Question 1

The principle of mathematical induction

Answer 1

Suppose that for each positive integer n we have a statement P(n). If we prove the following two things:
(A) P(1) is true;
(B) for all n, if P(n) is true, then P(n + 1) is also true;
then P(n) is true for all positive integers n ∈ N.

Question 2

The principle of mathematical induction (k)

Answer 2

Let k be an integer. Suppose that for each integer n ≥ k we have a statement P(n). If we prove the following two things:
(A) P(k) is true;
(B) for all n≥k, if P(n) is true, then P(n+1) is also true;
then P(n) is true for all integers n ≥ k.

Question 3

Summation notation

Question 4

Σ

Answer 4

Sigma (notation)

Question 5

Operations on sums

Answer 5

Prime factorisation ect