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Show that {:(" " Lt),( n rarroo):}1/n su...

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

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

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

{:(" "Lt),(n rarr oo):} {sum_(r=1)^(n)1/n e^(r//n)}=

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

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

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

{:(" "Lt),(n rarr oo):} sum_(r=1)^(n)((r^(3))/(r^(4)+n^(4)))=

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

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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