const data = {
  name: "数列",
  code: "sequence",
  source: "sequence",
  children: [
    {
      output: "a_{n}=a_{1}q^{n-1} ",
      source: "sequence_1",
    },
    {
      output: "a_{n}=a_{1}+ \\left( n-1 \\left) d\\right. \\right. ",
      source: "sequence_2",
    },
    {
      output: "S_{n}=na_{1}+\\frac{n \\eft( n-1 \\right)}{{2}}d ",
      source: "sequence_3",
    },
    {
      output: "S_{n}=\\frac{n \\left( a_{1}+a_{n}\\right)}{2} ",
      source: "sequence_4",
    },
    {
      output:
        "\\frac{1}{n \\left( n+k \\right)}= \\frac{1}{k}\\left( \\frac{1}{n}-\\frac{1}{n+k}\\right) ",
      source: "sequence_5",
    },
    {
      output:
        "\\frac{1}{n^{2}-1}= \\frac{1}{2}\\left( \\frac{1}{n-1}-\\frac{1}{n+1}\\right) ",
      source: "sequence_6",
    },
    {
      output:
        "\\frac{1}{4n^{2}-1}=\\frac{1}{2}\\left( \\frac{1}{2n-1}-\\frac{1}{2n+1}\\right) ",
      source: "sequence_7",
    },
    {
      output:
        "\\frac{n+1}{n \\left( n-1 \\left) \\cdot 2^{n}\\right. \\right.}= \\frac{1}{\\left( n-1 \\left) \\cdot 2^{n-1}\\right. \\right.}-\\frac{1}{n \\cdot 2^{n}} ",
      source: "sequence_8",
    },
    {
      output: `
\\begin{array}{c} 
  \\text{若}\\left \\{a_{n}\\right \\}、\\left \\{b_{n}\\right \\}\\text{为等差数列}, \\\\ 
  \\text{则}\\left \\{a_{n}+ b_{n}\\right \\}\\text{为等差数列} 
\\end{array}
      `,
      source: "sequence_9",
    },
    {
      output:
        "(1+x)^{n} =1 + \\frac{nx}{1!} + \\frac{n(n-1)x^{2}}{2!} + \\cdots ",
      source: "sequence_10",
    },
  ],
};

export default data;
