FunctionMedium
Question
If f(x) = {x} + { x + 1} + {x + 2} ....... {x + 99}, then the value of [f(√2) is, where {.} denotes fractional part function & [.] denotes the greatest integer function
Options
A.5050
B.4950
C.41
D.14
Solution
f(x) = x - [x] + (x + 1) - [x + 1] + .........
(x + 99) - [x + 99]
= x - [x] + x - [x] + ........... + x - [x]
= 100(x - [x]) = 100 {x}
f(√2) = 100{√2} = 41
(x + 99) - [x + 99]
= x - [x] + x - [x] + ........... + x - [x]
= 100(x - [x]) = 100 {x}
f(√2) = 100{√2} = 41
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