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Sum of series sin^2(xn)



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The solution

You have entered [src]
  6           
 ___          
 \  `         
  \      2/ n\
  /   sin \x /
 /__,         
n = 1         
$$\sum_{n=1}^{6} \sin^{2}{\left(x^{n} \right)}$$
Sum(sin(x^n)^2, (n, 1, 6))
The answer [src]
   2         2/ 2\      2/ 3\      2/ 4\      2/ 5\      2/ 6\
sin (x) + sin \x / + sin \x / + sin \x / + sin \x / + sin \x /
$$\sin^{2}{\left(x \right)} + \sin^{2}{\left(x^{2} \right)} + \sin^{2}{\left(x^{3} \right)} + \sin^{2}{\left(x^{4} \right)} + \sin^{2}{\left(x^{5} \right)} + \sin^{2}{\left(x^{6} \right)}$$
sin(x)^2 + sin(x^2)^2 + sin(x^3)^2 + sin(x^4)^2 + sin(x^5)^2 + sin(x^6)^2

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