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Question

=limn[1n+1n2+n+1n2+2n++1n2+(n1)n] is equal to [RPET 2000]


A
2+22
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B
222
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C
22
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D
2
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Solution

The correct option is B 222
y=limn[1n+1n2+n++1n2+(n1)n]
y=limn1n+1n1+1n++1n1+(n1)n
y=1nlimn1+11+1n++11+(n1)n
y=limn1nk=1n11+(k1)n, Put k1n=x and 1n=dx
y=limnn1n0 dx1+x=limn2[1+x](n1n)0
y=2limn[2n1n1]=2limn2n1n2
y=2 limn 21n2=222

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