Let (n ) be an integer such that (n 3 )

MATHEMATICS · Multi-part · CBSE · Mathematics · Permutations and Combinations · Permutations and Combinations

Problem

Let

n

be an integer such that

n \ge 3

. Define the three quantities:

A = (n+1)!

B = \bigl(n!\bigr)^2

C = \dfrac{(2n)!}{n!}.

(i) Simplify

C

so that no factorial remains in the denominator. (ii) Arrange

A,\,B,\,C

in ascending order of magnitude for every

n \ge 3

. (iii) Provide a rigorous justification for the ordering obtained in part (ii), making explicit reference to your simplification from part (i).