III] Sequences / functions

Question 1

What is the symbol of “summation”?

Answer 1

Σ

Question 2

ⁿΣ_i=1 = ?

Answer 2

ⁿΣ_i=1 = a₁+a₂+….a_n

Question 3

How to find the number of terms in a summation?

Answer 3

number of terms = m-n+1

Question 4

∀c∈ℝ, ⁿΣ_i=m(c.a_i) = ?

Answer 4

∀c∈ℝ, ⁿΣ_i=m(c.ai​) = c.(ⁿΣ_i=ma_i)

Question 5

∀c∈ℝ, ⁿΣ_i=m(a_i+b_i​) =

Answer 5

∀c∈ℝ, ⁿΣ_i=m(a_i​+b_i) =ⁿΣ_i=ma_i + ⁿΣ_i=mb_i

Question 6

ⁿΣ_i=1(1) = ?

Answer 6

= n

Question 7

ⁿΣ_i=1i = ?

Answer 7

= (n(n+1))/2

Question 8

ⁿΣ_k=0q^k = ?

Answer 8

ⁿΣ_k=0q^k = (1-qⁿ⁺¹)/1-q

if q≠1

Question 9

What are the 3 conditions for an induction reasoning?

Answer 9

1. Prove (a₁) or (a₀) is True
2. Prove that if (a_n) is True, then (a_n+1) is True. A_n=> A_n+1
3. By induction, ∀n, (A_n) is True

Question 10

What are the 3 elements needed to get a function?

Answer 10

1. 2 sets (not necessary numbers)
2. Ordered pairs: (x,y) ≠ (y,x)
3. A relation R, that is simply a subset of XxY

Question 11

What is a function?

Answer 11

Rule that associates some x∈X to, at most, 1 y∈Y.

f(x) = y

f=X→Y

x⟼f(x)

Each x produces only one image (y).