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Question

limx0[x]+[x2]+[x3]+...+[x2n+1]+n+11+[x2]+[x]+2x nϵN is equal to

A
n+1
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B
n
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C
1
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D
0
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Solution

The correct option is D 0
Using [x2n]=0 and [x2n+1]=1 for n=0,1,2,3.., we get
limx0[x]+[x2]+[x3]+...+[x2n+1]+n+11+[x2]+[x]+2x=limx01+01+...1+n+11+01+2x=0

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