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Question

Evaluate: limx(x+1)10+(x+2)10+..+(x+100)10x10+1010

A
10
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B
100
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C
1000
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D
1
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Solution

The correct option is B 100
Given: limx(x+1)10+(x+2)10+..+(x+100)10x10+1010

limx(x+1)10+(x+2)10+..+(x+100)10x10+1010
=limxx10((1+1x)10+(1+2x)10.....+(1+100x)10)x10(1+1010x10)
=limx((1+1x)10+(1+2x)10.....+(1+100x)10)(1+1010x10)

=1+0+1+0+....1+0(100 terms)1+0 [n1n0]

=1+1+....+(100 terms)1
=100

Hence option B is the answer.

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