-1の11乗根の1から10乗において，奇数乗を加え，偶数乗を引いた時の和

py.ipynb

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   "source": [
    "import sympy\n",
    "N = 10\n",
    "k = sympy.Symbol('k')\n",
    "sympy.summation((-1)**(k-1) * (-1)**(k/(N+1)), (k, 1, N)).simplify()"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/latex": [
       "$\\displaystyle - \\left(-1\\right)^{\\frac{6}{11}} - \\left(-1\\right)^{\\frac{4}{11}} - \\left(-1\\right)^{\\frac{8}{11}} - \\left(-1\\right)^{\\frac{2}{11}} - \\left(-1\\right)^{\\frac{10}{11}} + \\sqrt[11]{-1} + \\left(-1\\right)^{\\frac{9}{11}} + \\left(-1\\right)^{\\frac{3}{11}} + \\left(-1\\right)^{\\frac{7}{11}} + \\left(-1\\right)^{\\frac{5}{11}}$"
      ],
      "text/plain": [
       "-(-1)**(6/11) - (-1)**(4/11) - (-1)**(8/11) - (-1)**(2/11) - (-1)**(10/11) + (-1)**(1/11) + (-1)**(9/11) + (-1)**(3/11) + (-1)**(7/11) + (-1)**(5/11)"
      ]
     },
     "metadata": {},
     "execution_count": 1
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   "metadata": {}
  }
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