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Lt(ntooo)([1+4+9+......+n^(2)])/(n^(3))...

`Lt_(ntooo)([1+4+9+......+n^(2)])/(n^(3))`

A

2

B

3

C

`1//2`

D

`1//3`

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Evaluate the following limits : Lt_(ntooo)(1+2+3+......+n)/n^(2)

Lt_(ntooo)[(1)/(1+n^(3))+(4)/(8+n^(3))+(9)/(27+n^(3))+.......+(1)/(2n)]=

Lt_(ntooo)[(1)/(1+n^(2))+(2)/(1+n^(2))+.............+(n)/(1+n^(2))]

Lt_(ntooo)[(1)/(1-n^(2))+(2)/(1-n^(2))+.......+(n)/(1-n^(2))]=

Lt_(ntooo)[(n^(1//2))/(n^(3//2))+(n^(1//2))/((n+3)^(3//2))+(n^(1//2))/((n+6)^(3//2))+.......+(n^(1//2))/({n+3(n-1)}^(3//2))]=

Lt_(ntooo)[(1^(3))/(n^(4)+1^(4))+(2^(3))/(n^(4)+2^(4))+.........+(1)/(2n)]=

Evaluate the following limits : Lt_(ntooo)(1^(2)+2^(2)+3^(2)+......+n^(2))/n^(3)

Lt_(ntooo)[(sqrt(n^(2)-1^(2)))/(n^(2))+sqrt(n^(2)-2^(2))/(n^(2))+(sqrt(n^(2)+3^(2)))/(n^(2))+...........+nterms]=

Lt_(n-oo)[(1)/(n^(3))+(2^(2))/(n^(3))+.........+(n^(2))/(n^(3))]=

Lt_(n rarr oo)[(1n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+(n^(2))/((n+3))+...."to n terms"]

DIPTI PUBLICATION ( AP EAMET)-DEFINITE INTEGRATION-EXERCISE 1D
  1. Lt(ntooo){(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+.......+1/(n)}

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  2. Lt(n-oo)[(1)/(n^(3))+(2^(2))/(n^(3))+.........+(n^(2))/(n^(3))]=

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  3. Lt(ntooo)([1+4+9+......+n^(2)])/(n^(3))

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  4. Lt(ntooo)(1^(9)+2^(9)+3^(9)+.........+n^(9))/(n^(10))=

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  5. Evaluate the limit . underset(n to 00)("Lt") (1+2^(4)+3^(4)+…….+n^(4...

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  6. Lt(ntooo)sum(r=1)^(n)(1)/(n)e^(r//pi) is

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  7. Lt(ntooo)[(1)/(1+n^(3))+(4)/(8+n^(3))+(9)/(27+n^(3))+.......+(1)/(2n)]...

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

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  9. By the definition of the definite integral, the value of lim(ntooo)((...

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  10. Lt(ntooo){(sqrt1+sqrt2+sqrt3+.........+sqrtn)/(nsqrtn)}

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  11. Evaluate the limit. underset(n to 00)("lim") (sqrt(n+1)+sqrt(n+2)+…...

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  12. Lt(ntooo)[(sqrt(n^(2)-1^(2)))/(n^(2))+sqrt(n^(2)-2^(2))/(n^(2))+(sqrt(...

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  13. Lt(ntooo)[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt((2...

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  14. Lt(ntooo){(1)/(sqrt(n^(2)+1))+(1)/(sqrt(n^(2)+2^(2)))+.......+(1)/(sqr...

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

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  16. Lt(ntooo)(1)/(n){sin^(2)""(pi)/(2n)+sin^(2)""(2pi)/(2n)+..........+sin...

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  17. Lt(ntooo)(1)/(n)[sec^(2)""(pi)/(4n)+sec^(2)""(2pi)/(4n)+......+sec^(2)...

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

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  19. Evaluate underset(n to oo)("lim")[(1+(1)/(n))(1+2/n)* * * (1+(n)/(n))...

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

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