262should be n(n+1)/2 ≤ f(x)≤ n(n+1)/2 +1
What is Range of
f(x)=[1+sinx] + [2+ sin(x/2)] + [3+sin(x/3)]+........... + [n+ sin(x/n)]
for all x belongs to [0,∩] where [.] denotes greatest integer function?
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4 Answers
262in the given range , 0≤sin(x/r)≤1 where r→(1,n)
and [r + sin(x/r)] = r+1 (if x/r = pi/2)
else r
which is possible only once.