Prove the inequality using the Intermediate Value Theorem: (1)/(2√(n+1)) ≤ √(n+1) - √(n) ≤ (1)/(2√n)

Which of the following options correctly proves the inequality using the Intermediate Value Theorem?

A) (1)/(2√(n+1)) ≤ √(n+1) - √(n) ≤ (1)/(2√n)
B) √(n+1) - √(n) ≤ (1)/(2√(n+1)) ≤ (1)/(2√n)
C) √(n+1) - √(n) ≤ (1)/(2√n) ≤ (1)/(2√(n+1))
D) √(n+1) - √(n) ≤ (1)/(2√(n+1)) ≤ (1)/(2√n)

Note: The unnecessary space and unnecessary words have been removed to make the question more concise and clear.