Question

$\displaystyle \sf\lim_{x \to 0 } \frac{1 - \prod \limits_{k = 2}^{n} \sqrt[k]{cos(kx)} }{ {x}^{2} } = 10$​

Answer 1

First, let's note that for x∈(0,2π)x∈(0,2π)

∑k=1nsinkxk=∫x0∑k=1ncoskt dt=−x2+∫x0sin(2n+1)t22sint2 dt∑k=1nsin⁡kxk=∫0x∑k=1ncos⁡kt dt=−x2+∫0xsin⁡(2n+1)t22sin⁡t2 dt

=−x2+∫x0(12sint2−1t)sin(2n+1)t2 dt+∫

hope it helps you

mark as brainest and follow

Answer 2

Answer:

$\huge \purple{n = 6}$