高一数学(急啊)
来源:百度知道 编辑:UC知道 时间:2024/05/16 03:44:54
1.求数列的和:1/2+3/4+7/8+……+2^n-1/2^n
2.求数列的和:1/a+2/a^2+3/a^3+……+n/a^n
大家帮帮忙啊~~~
2.求数列的和:1/a+2/a^2+3/a^3+……+n/a^n
大家帮帮忙啊~~~
1/2+3/4+7/8+……+2^n-1/2^n
=1-1/2+1-1/4+...+1-1/2^n
=n-(1/2+1/4+...+1/2^n)
=2-(1-1/2^n)
=1+1/2^n
2题见图
1/2+3/4+7/8+……+(2^n-1)/2^n
=1-1/2+1-1/4+1-1/8+1-1/16+…+1-1/2^n
=n-(1/2+1/4+1/8+1/16+…+1/2^n)
=n-1/2(1/2^n-1)/(1/2-1)
=n+1/2^n-1
设S=1/a+2/a^2+3/a^3+……+n/a^n
aS=1+2/a+3/a^2+4/a^3+……+n/a^(n-1)
故:aS-S=(a-1)S=1+1/a+1/a^2+1/a^3+……+1/a^(n-1)- n/a^n
=(1/a^n-1)/(1/a-1) - n/a