If $I_n=\int_0^{\pi/4} \tan^n x\, dx$, then $\lim_{n\to\infty} n[I_n + I_{n+2}]$ equals
- A. $\frac{1}{2}$
- B. $1$
- C. $\infty$
- D. $0$
✅ Correct Answer: $1$
Explanation
Using the reduction formula and asymptotic analysis, as $n\to\infty$, $I_n\approx\frac{1}{n}$, giving the limit equal to 1.
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