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Lt(n rarr oo)[(1)/(n+1) + (1)/(n+2)+..(1...

`Lt_(n rarr oo)[(1)/(n+1) + (1)/(n+2)+..(1)/(2n)]`

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

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

Knowledge Check

  • {:(" "Lt),(n rarr oo):}[(1)/(na)+(1)/(na+1)+(1)/(na+2).......+(1)/(nb)]=

    A
    `log(b/a)`
    B
    `log(a/b)`
    C
    `log a`
    D
    `log b`

  • {:(" "Lt),(n rarr oo):}{ (1)/(2n+1)+(1)/(2n+2)+......+(1)/(3n)}=

    A
    `log_(e)(3/2)`
    B
    `log_(e)(2/3)`
    C
    `log_(e)(4/3)`
    D
    `log_(e)(1/3)`

    • Similar Questions

    Explore conceptually related problems

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

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

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

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

    Lt_(n rarr oo)[(1)/(n^(2))sec^(2)((1)/(n^(2)))+(2)/(n^(2))sec^(2)""((4)/(n^(2)))+(3)/(n^(2))sec((9)/(n^(2)))+....+(1)/(n)sec^(2)1]

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