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sum(n=1)^(n) (1)/((4 n-1)(4 / t+3))=...

`sum_(n=1)^(n) (1)/((4 n-1)(4 / t+3))=`

A

`(2 n)/(3(4 n+3))`

B

`3 n(4 n-1)`

C

`(n)/(3(3 n+4)`

D

`(n(n+1)^(2)(n+2))/(12)`

Text Solution

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The correct Answer is:
C
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If sum_(r=1)^(n)T_(r)=(n(n+1)(n+2)(n+3))/(12) where T_(r) denotes the rth term of the series. Find lim_(nto oo) sum_(r=1)^(n)(1)/(T_(r)) .

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Knowledge Check

  • If sum_(r=1)^(n) t_(r ) = sum_(k=1)^(n) sum_(j=1)^(k) sum_(i=1)^(j) 2 , then sum_(r=1)^(n) (1)/( t_(r )) equals :

    A
    `(n+1)/( n )`
    B
    `( n )/( n + 1)`
    C
    `(n-1)/( n ) `
    D
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  • If x^(2)-x+1=0 then the value of sum_(n=1)^(5)(x^(n)+(1)/(x^(n)))^(2) is

    A
    10
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    6
    D
    4

  • If 1+x^(2)=sqrt(3)x , then sum_(n=1)^(24)(x^(n)-(1)/(x^(n)))^(2) equals

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    D
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