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Statement -1 If Delta(r)=|{:(r,r+1),(r+3...

Statement -1 If `Delta(r)=|{:(r,r+1),(r+3,r+4):}|` then `sum_(r=1)^(n) Delta(r)=-3n`
Satement-2 If `Delta(r)|{:(f_(1)(r),f_(2)(r)),(f_(3)(r),f_(4)(r)):}|`
`Sigma_(r=1)^(n) Delta (r)={:abs((Sigma_(r=1)^(n)f_1(r),Sigma_(r=1)^(n)f_2(r)),(Sigma_(r=1)^(n)f_3(r),Sigma_(r=1)^(n) f_4(r))):}`

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Knowledge Check

  • Sigma_(r=0)^(n)((r^(2))/(r+1)).^(n)C_(r) is equal to

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

  • Sigma_(r=0)^(n)(n-r)(.^(n)C_(r))^(2) is equal to

    A
    `n^(2)(.^(2n-1)C_(n))`
    B
    `n^(2)(.^(2n)C_(n-1))`
    C
    `n^(2)(.^(2n-1)C_(n-1))`
    D
    `m^(2)(.^(2n-2)C_(n))`

  • Lt_(n rarr oo) Sigma_(r=1)^(n) (1)/(n) e^(r//n) =

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    e
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