A geometry problem by Rudraksh Sisodia

Geometry Level 4

$\large \prod_{k=1}^{100} \left[1+2\cos\left(\frac{2\pi(3^k)}{3^{100}+1}\right)\right] = \, ?$

The answer is 1.

1 solution

Hana Wehbi
Aug 27, 2016

We know the $cos$ part is going to $0$ at some point because $cos \frac{\pi}{2}=0$ ,so we are left with the product of 1 by itself $100$ times= $1$

my work was more tedious :(

Rudraksh Sisodia - 4 years, 9 months ago

My work is the lazy one. I like simple solutions but I enjoy a lot the long hard ones written by others :)

Hana Wehbi - 4 years, 9 months ago

btw i am very poor in latex ,, thus i cannot upload the solution .. :(

Rudraksh Sisodia - 4 years, 9 months ago

@Rudraksh Sisodia – No worries, I just learnt Latex few months ago, I totally understand how does it feel to write complicated symbols using Latex. It is painful :)

Hana Wehbi - 4 years, 9 months ago

A geometry problem by Rudraksh Sisodia

The answer is 1.

1 solution

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