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Question

Let I1=n0[x]dx and I2=n0{x}dx, where [x] and {x} are integral and fractional parts of x and nϵN{1}. Then I1/I2 is equal to

A
1n1
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B
1n
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C
n
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D
n1
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Solution

The correct option is A n1
I1=n0[x]dx=100 dx+211dx+322dx+....+nn1(n1)dx

=0+(21)+2(32)+3(43)+......+(n1)(n(n1))
=0+1+2+3+.....+(n1)
=n(n1)2,
I2=n0{x}dx
=n0x dxn0[x]dx
=n0x dxI1
=n22n(n1)2=n2
I1/I2=n1

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