Published by:
CGP EDU Academic Team
Published on: August 11, 2026
Evaluate 
, where [ . ] denotes greatest integer function.
Text Solution
Verified by ExpertsThe correct answer is:
1
( 
)
Sol. 
(1.2)x – 1 < [1.2x] ≤ (1. 2)x
(2.3)x – 1 < [2.3x] ≤ (2.3)x
n(n + 1) x – 1 < [n (n + 1)x] ≤ n(n + 1)x
so (1.2)x + (2.3)x + ... n (n + 1)x – n
< [1.2 x] + [2. 3 x] + .... [n(n +1)x]
≤ (1. 2) x + (2. 3) x + .... n(n +1)x
x . ( Σ n 2 + Σ n) – n ≤ [1. 2x] + [2. 3x] +......[n(n+1)x] ≤ x ( Σ n 2 + Σ n)
⇒ 
< 
× 
≤ 
× 
so 
= 
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