Question

Assuming \( x \) is a whole number greater than or equal to 2, arrange the above four in decreasing order, with the largest first and smallest last:
(a) \(\frac{1}{x}\)
(b) \(\frac{1}{x^2}\)
©  \(\frac{1}{1+x}\)
(d)  \(\frac{1}{(1+x)^2}\)

• A. (A), (C), (B), (D)
• B. (B), (A), (B), (C), (D)
• C. (D), (B), (C), (A)
• D. (A), (D), (C), (B)

Hint:

When x ≥ 2, terms with higher denominators become smaller, and their value decreases accordingly.

Answer 1

The Correct Option is A

For \( x \geq 2 \), the order of the expressions from largest to smallest is:

• (A) \( \frac{1}{x} \) 
• (C) \( \frac{1}{1+x} \) 
•  (B) \( \frac{1}{x^2} \) 
•  (D) \( \frac{1}{(1+x)^2} \) 

Thus, the correct order is \((A), (C), (B), (D) . \)
\( \textbf{Hence, the correct answer is (a).}\)