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lim(n to oo) (n^(p) sin^(2)(n!))/(n +1) ...

`lim_(n to oo) (n^(p) sin^(2)(n!))/(n +1) , 0 lt p lt 1`, is equal to-

A

0

B

`oo`

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
1
`underset(nto oo) "lim" (n^(p) sin^(2) n!)/( n(1+I//n))`
`underset(nto oo) "lim" (n^(p-1) sin^(2) n!)/((1+I//n))= ((oo)^(p-1) [0,I])/(1) `
`= 0 xx [0, 1]=0`
` because plt1, p-1 lt0`
` oo^(-ve) =0`
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