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

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

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The correct Answer is:
`(2^(k))/(k+1)`
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{:(" "Lt),(n rarr oo):} ((1+2^(4)+3^(4)+......+n^(4))/(n^(5)))-{:(" "Lt),(n rarr oo):} ((1+2^(3)+3^(3)+....+n^(3))/(n^(5)))=

Evaluate lim_(n rarr oo)(2^(k) + 4^(k) + 6^(k)+…+(2n)^(k))/(n^(k+1)) by using the method of finding definite integral as the limit of a sum.

lim_(n toinfty)[(1^(k) +2^(k)+3^(k) +. . .. +n^(k))/(n^(k +1))]=

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

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

{:(" "Lt),(n rarr oo):} 1/n sum_(r=1)^(n)sec^(2).(rpi)/(4n)=

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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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