求数列3,7,15,31...的通项公式,求详解.求朋友们帮忙
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求数列3,7,15,31...的通项公式,求详解.求朋友们帮忙
![求数列3,7,15,31...的通项公式,求详解.求朋友们帮忙](/uploads/image/z/18210957-69-7.jpg?t=%E6%B1%82%E6%95%B0%E5%88%973%2C7%2C15%2C31...%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%2C%E6%B1%82%E8%AF%A6%E8%A7%A3.%E6%B1%82%E6%9C%8B%E5%8F%8B%E4%BB%AC%E5%B8%AE%E5%BF%99)
a2-a1=21,a3-a2=22,a4-a3=23,…依次类推可得an-an-1=2n-1
∴a2-a1+a3-a2+a4-a3…+an-an-1=an-a1=21+22+23+…+2n-1=2n-2
∴an-a1=2n-2,an=2n-1
故答案为2n-1
∴a2-a1+a3-a2+a4-a3…+an-an-1=an-a1=21+22+23+…+2n-1=2n-2
∴an-a1=2n-2,an=2n-1
故答案为2n-1