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Let S (n ) = sum ( k =0) ^(n) (1)/( sqr...

Let ` S _(n ) = sum _( k =0) ^(n) (1)/( sqrt ( k +1) + sqrt k)` What is the value of `sum _( n -1) ^( 90) (1)/( S _(n ) + S _( n -1)) ?=`

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Knowledge Check

  • sum_(k =1)^(n) k(1 + 1/n)^(k -1) =

    A
    `n(n -1)`
    B
    `n(n + 1)`
    C
    `n^(2)`
    D
    `(n +1 )^(2)

  • The value of cot (sum_(n=1)^(23) cot^(-1) (1 + sum_(k=1)^(n) 2k)) is

    A
    `(23)/(25)`
    B
    `(25)/(23)`
    C
    `(23)/(24)`
    D
    `(24)/(23)`

  • Let S_(n) = sum_(k=1)^(4n) (-1) (k(k-1))/(2), k^(2) . Then S_n can take values

    A
    `1056`
    B
    `1088`
    C
    `1120`
    D
    `1332`

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