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If alpha,beta are the roots of x^(2)+x+1...

If `alpha,beta` are the roots of `x^(2)+x+1=0`, and `s_(n)=alpha^(n)+beta^(n)`, then `|[3,1+S_(1),1+S_(2)],[1+S_(1),1+S_(2),1+S_(3)],[1+S_(2),1+S_(3),1+S_(4)]|=?`

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Knowledge Check

  • If alpha, beta are roots of 375x^(2)-25x-2=0 and s_(n)=alpha^(n)+beta^(n) , then lim_(n to oo) sum_(r=1)^(n)S_(r) is

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    `0`
    B
    `a+b+c`
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    `(a+b+c)n`
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    `n^(2)abc`

  • If alpha,beta are roots of 375x^2 - 25x -2 = 0 and s_n = alpha^n + beta^n , then lim_(n to oo)sum_(r = 1)^n S_r is

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