If `L=-lim_(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^(2)+1)))`, then the value of `L^(4)` is _____________.A. `-(1)/(4)`B. `(1)/(2)`C. 1D. 2

If `L=-lim_(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((

1.	If `L=-lim_(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^(2)+1)))`, then the value of `L^(4)` is _____________.A. `-(1)/(4)`B. `(1)/(2)`C. 1D. 2
Answer» Correct Answer - `(6)` Clearly, n is even. Then, `underset(ntooo)lim"("2^(1+3+5+...+n//2" terms ").3^(2+4+6+...+n//2" terms")")"^((1)/((n^(2)+1)))` `=underset(ntooo)lim(2^((n^(2))/(4)).3^((n(n+2))/(4)))^((1)/((n^(2)+1)))` `=2^(underset(ntooo)lim(1)/(4(1+(1)/(n^(2))))).3^(underset(ntooo)lim((1+(2)/(n)))/(4(1+(1)/(n^(2)))))` `=2^((1)/(4))3^((1)/(4))=(6)^((1)/(4))`

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