Question
The value of 
,where [x] denotes the greatest integer not exceeding x is
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af(a) − {f(1) + f(2) + … + f([a])}
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[a] f(a) − {f(1) + f(2) + … + f([a])}
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[a] f([a]) − {f(1) + f(2) + … + f(a)}
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af([a]) − {f(1) + f(2) + … + f(a)}
Solution
B.
[a] f(a) − {f(1) + f(2) + … + f([a])}
Let a = k + h, where [a] = k and 0 ≤ h < 1
{f(2) − f(1)} + 2{f(3) − f(2)} + 3{f(4) − f(3)}+…….+ (k−1) – {f(k) − f(k − 1)} + k{f(k + h) − f(k)}
= − f(1) − f(2) − f(3)……. − f(k) + k f(k + h)
= [a] f(a) − {f(1) + f(2) + f(3) + …. + f([a])}
