1.(a-1)+(a的平方-2)+...+=(a的n次幂-n)求和2.(2-3×5﹣¹)+(4-3×5﹣²)+…+(2n-3×5的-n次幂)求和上课老师说的听不懂,
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/28 12:03:57
![1.(a-1)+(a的平方-2)+...+=(a的n次幂-n)求和2.(2-3×5﹣¹)+(4-3×5﹣²)+…+(2n-3×5的-n次幂)求和上课老师说的听不懂,](/uploads/image/z/267853-13-3.jpg?t=1.%28a-1%29%2B%28a%E7%9A%84%E5%B9%B3%E6%96%B9-2%29%2B...%2B%3D%28a%E7%9A%84n%E6%AC%A1%E5%B9%82-n%29%E6%B1%82%E5%92%8C2.%EF%BC%882-3%C3%975%EF%B9%A3%26%23185%3B%EF%BC%89%2B%EF%BC%884-3%C3%975%EF%B9%A3%26%23178%3B%EF%BC%89%2B%E2%80%A6%2B%EF%BC%882n-3%C3%975%E7%9A%84-n%E6%AC%A1%E5%B9%82%EF%BC%89%E6%B1%82%E5%92%8C%E4%B8%8A%E8%AF%BE%E8%80%81%E5%B8%88%E8%AF%B4%E7%9A%84%E5%90%AC%E4%B8%8D%E6%87%82%2C)
1.(a-1)+(a的平方-2)+...+=(a的n次幂-n)求和2.(2-3×5﹣¹)+(4-3×5﹣²)+…+(2n-3×5的-n次幂)求和上课老师说的听不懂,
1.(a-1)+(a的平方-2)+...+=(a的n次幂-n)求和
2.(2-3×5﹣¹)+(4-3×5﹣²)+…+(2n-3×5的-n次幂)求和
上课老师说的听不懂,
1.(a-1)+(a的平方-2)+...+=(a的n次幂-n)求和2.(2-3×5﹣¹)+(4-3×5﹣²)+…+(2n-3×5的-n次幂)求和上课老师说的听不懂,
1..(a-1)+(a^2-2)+...+(a^n-n)
=(a+a^2+……+a^n)-(1+2+……+n)
前一项是公比为a的等比数列,后一项是公差为1的等差数列.
当a=1时,和sn=n-n(n+1)/2
当a不为1时,sn=a(1-a^n)-n(n+1)/2
2..(2-3×5﹣¹)+(4-3×5﹣²)+…+(2n-3×5^-n)
=2(1+2+…+n)-3(5﹣¹+5﹣²+…+5^-n)
前一项是一个公差为1的等差数列,后一项是一个以1/5为公比的等比数列
所以sn=2*n(n+1)/2-3*(1/5)(1-(1/5)^2)
=n(n+1)-3*(1/5)(1-(1/5)^2)