For x ε (0, π/2) and sin x = 1/3,
if \sum_{n=0}^{\infty }\frac{sin(nx)}{3^{n}}=\frac{a+b\sqrt{b}}{c}
then find the value of (a + b + c), where a, b, c are positive integers.
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3 Answers
2305Σsin(nx)3n = imaginary part of Σeinx3n = 11-eix3
Here, eix = 2√23+i3
On simplifying the RHS we get,
Σsin(nx)3n = 5+2√234
a+b+c = 41
