高一数学必修五等比数列.

a(n+1)=2an+2^n等式两边同除以2^na(n+1)/2^n=an/2^(n-1) +1a(n+1)/2^n -an/2^(n-1)=1,为定值。a1/2^(1-1)=1/1=1数列{an/2^(n-1)}是以1为首项,1为公差的等差数列。an/2^(n-1)=1+n-1=nan=n×2^(n-1)b1=a1/2^(1+1)=1/4bn=an/2^(n+1)=n×2^(n-1)/2^(n+1)=n/4b(n+1)-bn=(n+1)/4-n/4=1/4,为定值。数列{bn}是以1/4为首项,1/4为公差的等差数列。2、an=n×2^(n-1)Sn=a1+a2+。。。+an=1×2^0+2×2^1+3×2^2+。。。+n×2^(n-1)2Sn=1×2^1+2×2^2+。。。+(n-1)×2^(n-1)+n×2^nSn-2Sn=-Sn=2^0+2^1+2^2+。。。+2^(n-1)-n×2^n=(2^n -1)/(2-1) -n×2^n=(1-n)×2^n -1Sn=(n-1)×2^n +1