Prove that (a+b)/(an - bn) , if n is a positive even integer.

Amna Mughal

Prove that (a+b)/(an - bn) , if n is a positive even integer.

Prove that (a+b)/an-bn , if n is a positive even integer Proof: We prove it with the help of mathematical induction. CASE – I ...

Read more

Prove that product of three consecutive integers is divisible by 6.

Amna Mughal

Prove that product of three consecutive integers is divisible by 6.

Proof: The product of three consecutive integers which are divisible by 6 is: ⟹ 6 /n(n+1)(n+2) We have to prove it by mathema...

Read more

Prove that if n is an odd integer then 8/n^2 -1.

Amna Mughal

Prove that if n is an odd integer then 8/n^2 -1.

Theorem: Prove that if n is an odd integer then 8/n^2 -1. Proof: We prove it by mathematical induction CASE-I For n=1 = n^2 -1...

Read more

Show that (a-b)/(an -bn) for all n greater than and equal to Zero and belongs to Z.

Amna Mughal

Show that (a-b)/(an -bn) for all n greater than and equal to Zero and belongs to Z.

1 2

Read more

If a, b belongs to Z then show that (1) if a/b and b/a this implies a = ±b. (2) if a/b and b/c then a/c. (3) if a/b then a/bc. (4) if a/b then ac/bc. (5) if a/b and a/c then a/bx+cy for x,y belongs to Z. (6) if a/b1+b2 and a/b1 then a/b2. (7) a/o (8) 1/a

Amna Mughal

If a, b belongs to Z then show that (1) if a/b and b/a this implies a = ±b. (2) if a/b and b/c then a/c. (3) if a/b then a/bc. (4) if a/b then ac/bc. (5) if a/b and a/c then a/bx+cy for x,y belongs to Z. (6) if a/b1+b2 and a/b1 then a/b2. (7) a/o (8) 1/a

Theorem: If a, b belongs to Z then show that  If a/b and b/a this implies a = ±b.  If a/b and b/c then a/c. If a/b then a/bc. If a/b...

Read more

Euclid's Theorem and Its consequence

Amna Mughal

Euclid's Theorem and Its consequence

Definition: Set of integers is denoted by Z and defined as: Z = {0, ±1,  ±2,  ±3,... } Set of positive integers   Z+  = {1, 2, 3, ...

Read more