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{:(" " Lt),(n rarroo):} [(1^(2))/(n^(3)...

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

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{:(" " Lt),(n rarroo):} sum_(r=1)^(n)(r)/(n^(2)+r^(2))=

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

{:(" " Lt),(n rarroo):}(1)/(n^(2)) sum_(r=1)^(n) r.e^(r//n)=

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

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

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

{:(" " Lt),(n rarroo):} ((1+8+27+.......+n^(3))/(n^(4)))=

AAKASH SERIES-DEFINITE INTEGRALS-EXERCISE - 2.4
  1. Evaluate the following define integrals as limit of sums : int(0)^(1...

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  2. Evaluate the following define integrals as limit of sums : int(0)^(...

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  3. Evaluate the following define integrals as limit of sums : int(0)^(...

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  4. Evaluate the following define integrals as limit of sums : int(0)^(...

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  5. Evaluate the following definite integrals as limit of sums. int(0)^(...

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  6. Evaluate the following define integrals as limit of sums : int(0)^(...

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  7. Evaluate the following define integrals as limit of sums : lim(n rar...

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

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  9. Evaluate the following define integrals as limit of sums : lim(n rar...

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

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

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  12. Evaluate the following define integrals as limit of sums : lim(n rar...

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  13. Evaluate the following define integrals as limit of sums : lim(n ra...

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  14. Evaluate the following define integrals as limit of sums : lim(n ra...

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  15. Evaluate the following define integrals as limit of sums : lim(n ra...

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

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  17. Evaluate the following define integrals as limit of sums : lim( n r...

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  18. Show that {:(" " Lt),( n rarroo):}1/n sum(r=1)^(n) sec^(2) .(r pi)/(4n...

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  19. {:(" " Lt),(n rarroo):} [(1^(2))/(n^(3)+1^(3))+(2^(2))/(n^(3)+2^(3))+...

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