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Byju's Answer

Standard XII

Mathematics

Signum Function

If [x] and x ...

Question

If [x] and {x} represent integral and fractional parts of x, then the expression $[x] + 2000 \sum r = 1 \frac{{x + r}}{2000}$ is equal to

\frac{2001}{2} x

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x + 200

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x

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[x] + \frac{2001}{2}

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Solution

The correct option is C $x$
$[x] + 2000 \sum r = 1 \frac{{x + r}}{2000}$
$[x] + \frac{{x + 1}}{2000} + \frac{{x + 2}}{2000} + . . . . . . . . + \frac{{x + 2000}}{2000}$
$[x] + \frac{2000 {x}}{2000} = x$

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If [x] and {x} represent integral and fractional parts of x, then the expression [x]+2000∑r=1{x+r}2000 is equal to

The correct option is C x[x]+2000∑r=1{x+r}2000[x]+{x+1}2000+{x+2}2000+........+{x+2000}2000[x]+2000{x}2000=x

If [x] and {x} represent integral and fractional parts of x, then the expression $[x] + 2000 \sum r = 1 \frac{{x + r}}{2000}$ is equal to

The correct option is C $x$
$[x] + 2000 \sum r = 1 \frac{{x + r}}{2000}$
$[x] + \frac{{x + 1}}{2000} + \frac{{x + 2}}{2000} + . . . . . . . . + \frac{{x + 2000}}{2000}$
$[x] + \frac{2000 {x}}{2000} = x$