Let fn(θ)= displaystyle∑n=0n (1/4n) sin 4(2n θ). Then which of the following alternative (s) is/are correct?

Question

Let fn(θ)= displaystyle∑n=0n (1/4n) sin 4(2n θ). Then which of the following alternative (s) is/are correct? (A) f 2((π/4))=(1/√2) (B) f 3((π/8))=(2+√2/4) (C) f 4((3 π/2))=1 (D) f 5(π)=0

Tardigrade Admin · Accepted Answer

Correct answer is (c) f 4((3 π/2))=1Correct answer is (d) f 5(π)=0

Q. Let $f_{n} (θ) = n = 0 \sum n \frac{1}{4 ^{n}} sin^{4} (2^{n} θ)$ . Then which of the following alternative (s) is/are correct?

$f_{2} (\frac{π}{4}) = \frac{1}{2}$

$f_{3} (\frac{π}{8}) = \frac{2 + 2}{4}$

$f_{4} (\frac{3 π}{2}) = 1$

$f_{5} (π) = 0$

Correct answer is (c) $f_{4} (\frac{3 π}{2}) = 1$ Correct answer is (d) $f_{5} (π) = 0$

Q. Let fn​(θ)=n=0∑n​4n1​sin4(2nθ). Then which of the following alternative (s) is/are correct?

f2​(4π​)=2​1​

f3​(8π​)=42+2​​

f4​(23π​)=1

f5​(π)=0