PRINCIPLE OF MATHEMATICAL INDUCTION + BINOMIAL THEOREM

Question 1

Steps in Mathematical Induction (4)

Answer 1

1. Show that P_n is true for n = 1
2. Inductive Hypothesis
   (assume that P_n = [FORMULA] is true for n = k)
3. Show that P_n = [FORMULA] is true for n = k + 1
4. Final statement

Question 2

(3a-2)^4

Answer 2

81a^4 - 216a^3 + 216a^2 - 96a + 16

Question 3

Formula for binomial coefficient

Answer 3

(n k)

Question 4

Binomial Theorem

Answer 4

n (sigma) k = 0 (n k) x^(n-k)y^k

Question 5

(n k) =

Answer 5

n! / k! (n-k)!