The value of (1-1/3) (1-1/4)(1-1/5) ..... (1-1/n) is equal to :

Correct option is B

Solution to the Problem

Problem:

Find the value of the expression:
(1 - 1/3) (1 - 1/4) (1 - 1/5) ... (1 - 1/n).

Solution:

Step 1: Simplify each term

Each term in the product can be simplified as follows:
1 - 1/k = (k - 1) / k, where k ≥ 3.
Thus, the product becomes:
(1 - 1/3) (1 - 1/4) (1 - 1/5) ... (1 - 1/n)
= (2/3) × (3/4) × (4/5) × ... × ((n-1)/n).

Step 2: Combine terms

The product telescopes (cancels out adjacent terms) as follows:
(2/3) × (3/4) × (4/5) × ... × ((n-1)/n)
= 2/n.

Final Answer:

The value of the expression is:
(1 - 1/3) (1 - 1/4) (1 - 1/5) ... (1 - 1/n) = 2/n.