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

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

A

`log(2//3)`

B

`log(3//2)`

C

`log(4//3)`

D

none

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Lt_(ntooo){(1)/(n)+(1)/(n+1)+(1)/(n+2)+.......+(1)/(3n)}=

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{:(" " Lt),(n rarroo):} [(1)/(3n+1)+(1)/(3n+2)+.......+(1)/(4n)]=

Lt_(ntooo){(1)/(n)+(1)/(n+1)+(1)/(n+2)+.......+(1)/(4n)}=

Lt_(ntooo){(1)/(2n+1)+(1)/(2n+2)+(1)/(2n+3)+..........+(1)/(2n+n)}=

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

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

Lt_(ntooo)sum_(r=0)^(n-1)(1)/(n+r)=

Lt_(n rarr oo)[(1)/(3n+1) + (1)/(3n+2)+…+(1)/(4n)]

Evaluate Lt_(n rarr oo) ((1)/(n+1) + (1)/(n+2) +..+(1)/(3n))

DIPTI PUBLICATION ( AP EAMET)-DEFINITE INTEGRATION-EXERCISE 1D
  1. Lt(ntooo){(1)/(n)+(1)/(n+1)+(1)/(n+2)+.......+(1)/(3n)}=

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  2. Lt(ntooo){(1)/(2n+1)+(1)/(2n+2)+(1)/(2n+3)+..........+(1)/(2n+n)}=

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  3. Lt(ntooo)[(1)/(3n+1)+(1)/(3n+2)+............+(1)/(3n+n)]=

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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