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{:(" "Lt),(n rarr oo):} ((1^(m)+2^(m)+3^...

`{:(" "Lt),(n rarr oo):} ((1^(m)+2^(m)+3^(m)+.........+n^(m))/(n^(m+1)))=`

A

`(1)/(m+1)`

B

`(1)/(m+2)`

C

`(1)/(m)`

D

`(1)/(m+3)`

Text Solution

Verified by Experts

The correct Answer is:
A
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AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - II
  1. {:(" "Lt),(n rarr oo):}[(1)/(na)+(1)/(na+1)+(1)/(na+2).......+(1)/(nb)...

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  2. {:(" "Lt),(n rarr oo):}{ (1)/(2n+1)+(1)/(2n+2)+......+(1)/(3n)}=

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  3. {:(" "Lt),(n rarr oo):} ((1^(m)+2^(m)+3^(m)+.........+n^(m))/(n^(m+1))...

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  4. {:(" "Lt),(n rarr oo):} ((1+2^(4)+3^(4)+......+n^(4))/(n^(5)))-{:(" "L...

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  5. {:(" "Lt),(n rarr oo):} (2^(k)+4^(k)+6^(k)+....+(2n)^(k))/(n^(k+1))=

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  6. Lt(ntooo)[(1^(3))/(n^(4)+1^(4))+(2^(3))/(n^(4)+2^(4))+.........+(1)/(2...

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  7. Lt(ntooo){(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+.......+1/(n)}

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  8. {:(" "Lt),(n rarr oo):} [ (1)/(n^(2)) sec^(2). (1)/(n^(2)) + (2)/(n^(2...

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  9. {:(" "Lt),(n rarr oo):} ((sqrt(1)+2sqrt(2)+3sqrt(3)+......+nsqrt(n))/(...

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  10. {:(" "Lt),(n rarr oo):} [(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)...

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  11. {:(" "Lt),(n rarr oo):} ((1)/(sqrt(4n^(2)-1))+(1)/(sqrt(4n^(2)-2^(2)))...

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  12. {:(" "Lt),(n rarr oo):} ((1)/(sqrt(2n-1^(2)))+(1)/(sqrt(4n-2^(2)))+(1)...

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  13. {:(" "Lt),(n rarr oo):} ((1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)+n))+(1)/(sq...

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  14. Lt(ntooo)[(n^(1//2))/(n^(3//2))+(n^(1//2))/((n+3)^(3//2))+(n^(1//2))/(...

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  15. If S(n)={(1)/(1+sqrt(n))+(1)/(2+sqrt(2n))+(1)/(3+sqrt(3n))+....+(1)/(n...

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  16. {:(" "Lt),(n rarr oo):} 3/n [1 + sqrt((n)/(n+3))+sqrt((n)/(n+6))+sqrt(...

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  17. {:(" "Lt),(n rarr oo):} ((n!)/(n^(n)))^(1/n)=

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  18. Evaluate the limit . underset(n to 00)("lim") [(1+(1)/(n^(2)))(1+(2^...

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  19. If f(n)= 1/n {(n+1)(n+2)....2n}^(1//n) then {:(" "Lt),(n rarr oo):} f(...

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  20. {:(" "Lt),(n rarr oo):}(((2n)!)/(n!n^(n)))^(1/n)=

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