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Sum of the series `Sigma_(r=1)^(n) rlog((r+1)/(r))` isA. `log[((n+1)^(n))/(n!)]`B. `(log(n+1)^(n))/(n!)`C. `n!log(n+1)`D. None of these |
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Answer» Correct Answer - A Using `C_(1)rarrC_(1)+C_(2)+C_(3), " we get " Delta=2|(y+z,z,y),(z+x,z+x,x),(x+y,x,x+y)|` Using `C_(2)rarrC_(2)-C_(1),C_(3)rarrC_(3)-C_(1)`,we get `Delta=2|(y+z,-y,-z),(z+x,0,-z),(x+y,-y,0)|=2|(0,-y,-z),(x,0,-z),(x,-y,0)|" "["Using"C_(1)rarrC_(1)+C_(2)+C_(3)]` `=2xyz |(0,1,1),(1,0,1),(1,1,0)|=4xyz` `"Now "4xyz=12impliesxyz=3` The number 3 can be assigned to any of x,y,z. Therefore, the number of positive integral solution of `Delta=12` to 3. |
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