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

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Question

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

${1 \over 2}$

$1$

$\infty $

zero

Solution

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