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Question

Let Sn=nl=1(l4+l3n+l2n2+2n4n5) andTn=n1l=0(l4+l3n+l2n2+2n4n5),(n=1,2,3,...)then

A
Tn>16760
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B
Tn<16760
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C
Sn>16760
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D
Sn<16760
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Solution

The correct option is C Sn>16760
Replace lnx and1ndx, The functoin we get is f(x)=x4+x3+x2+2
f(x) is increasing in (0,1)
Sn=nl=1l4n4.1n+l3n3.1n+l2n2.1n+2n

(Sn is the sum of all the rectangles
>10(x4+x3+x2+2) dx (Sn>area under curve)=16760
Sn>16760


Tn=n1l=0(l4+l3n+l2n2+2n4n5) (Tn< area under curve)
Tn<10f(x)dx
Tn<16760

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