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`lim_(ntoprop) (n)/(3){((3)/(n)+(9)/(n^(2)))^(2)+((3)/(n)+(18)/(n^(2)))^(2)+((3)/(n)+(27)/(n^(2)))^(2)+….+((3)/(n)+(9)/(n))^(2)}` is less than or equal toA. 62B. 63C. 14D. 21 |
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Answer» Correct Answer - A::B::D `underset(nto prop)(lim)sum_(r-1)^(n)(n)/(3)((3)/(n)+(9r)/(n^(2)))^(2)` `underset(nto prop)(lim)sum_(r=1)^(n)(n)/(3).(9)/(n^(2))(1+(3r)/(n))^(2)` `underset(nto prop)(lim)sum_(r=1)^(n)(3)/(n)(1+(3r)/(n))^(2)` `3int_(0)^(1)(1+3x)^(2)dx` `(cancel(3)(1+3x)^(3))/(cancel(3).3))_(0)^(1)` `(64)/(4)-(1)/(3)=21` |
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