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Question

The value of limx0[x]+[x2]+[x3]+....+[x2n+1]+n+11+[x2]+|x|+2x, n N 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
When x0, we have
[x2n+1]=1 and [x2n]=0 for n=0,1,2,....
limx0[x]+[x2]+[x3]+....+[x2n+1]+n+11+[x2]+|x|+2x
=limx0(1)+0+(1)+0+....+0+(1)+n+11+0x+2x
=limx0(1)(n+1)+n+11+x
=01+0=0

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