Proofs

Question 1

Prove that sum of terms in a geometric series are Sn=a(1-r^n)/1-r

Answer 1

Check book

Question 2

Prove that sun if terms in an arithmetic series is n/2(2a+(n-1)d)

Answer 2

Check book

Question 3

Prove that if (x-p) is a factor of f(x) then f(p)=0

Answer 3

Check book

Question 4

Prove by contradiction that there are infinite prime numbers

Answer 4

Check book

Question 5

Prove by contradiction that 2 is an irrational number

Question 6

Prove from first principles that the derivative of X^3 is 3X^2

Answer 6

Check book

Question 7

What is prove by deduction

Answer 7

Starting from definitions eg using 2p+1 as an odd number

Question 8

What is proof by exhaustion

Answer 8

Breaking statement into smaller cases and proving each and every bit eg split into odd number and even

Question 9

What is proof by counter example

Answer 9

Giving one example that does not work for the statement

Question 10

What is proof by contradiction Gino

Answer 10

Start by assuming statement is not true and show that this is impossible

Question 11

What is a rational number

Answer 11

Can be represented as a/b with intergers