JEE MAIN - Mathematics Hindi (2002 - No. 18)

$${I_n} = \int\limits_0^{\pi /4} {{{\tan }^n}x\,dx} $$ तब $$\,\mathop {\lim }\limits_{n \to \infty } \,n\left[ {{I_n} + {I_{n + 2}}} \right]$$ बराबर है