Problem of the Day #79


POTD February 25, 2024

n=0sin(nx)3n\sum\limits_{n=0}^\infty\frac{\sin (nx)}{3^n}, if sinx=1/3\sin x=1/3 and 0xπ20 \leq x\leq \frac{\pi}{2}, can be written as a+bcd\frac{a+b \sqrt c}{d}, where cc is a positive integer not divisible by the square of any prime and a,b,ca,b,c are positive integers such that gcd(a,b,c)=1\gcd (a,b,c)=1. Find a+b+c+da+b+c+d.

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Category: Problem of the Day
Points: 4
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