Question

Let $f_n(\theta)=\displaystyle\sum_{n=0}^n \frac{1}{4^n} \sin ^4\left(2^n \theta\right)$. Then which of the following alternative (s) is/are correct?

• A. $f _2\left(\frac{\pi}{4}\right)=\frac{1}{\sqrt{2}}$
• B. $f _3\left(\frac{\pi}{8}\right)=\frac{2+\sqrt{2}}{4}$
• C. $f _4\left(\frac{3 \pi}{2}\right)=1$
• D. $f _5(\pi)=0$

Answer 1

Answer: (C), (D)

Correct answer is (c) $f _4\left(\frac{3 \pi}{2}\right)=1$Correct answer is (d) $f _5(\pi)=0$