Let {x} and [x] denote the fractional part of x and the greatest integer ≤ x respectively of a real number x. if ∫(from 0 to n){x}dx, ∫(from 0 to n)[x]dx and 10(n² – n), (n ∈ N, n > 1) are three consecutive terms of a G.P. then n is equal to
Let {x} and [x] denote the fractional part of x and the greatest integer ≤ x respectively of a real number x. if ∫(from 0 to n){x}dx, ∫(from 0 to n)[x]dx and 10(n² – n), (n ∈ N, n > 1) are three consecutive terms of a G.P. then n is equal to
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1 Answer
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Clearly, ∫ [0 to n] {x}dx = n/2
∫ [0 to n] [x]dx = 1 + 2 + 3 . . . n − 1
= n (n-1)/2
∴ (n (n-1)/2)² = n/2 {10n (n-1)}
Solving, n = 21
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