bn=a1+2a2+3a3+4a4+……+nan若an是等差数列，则bn=？

显示全部楼层 · 2011-9-30 17:34:56

数列｛an｝是正项等差数列，若bn＝(a1+2a2+3a3+…+nan)/(1＋2＋3＋…+n)，则数列｛bn｝也为等差数列?设an公差为d，则bn=(a1+2a2+3a3+…+nan)/(1+2+3+…+n)=2(a1+2a2+3a3+…+nan)/n(n+1)=2(a1+2(a1+d)+3(a1+2d)+…+n(a1+(n-1)d)/n(n+1)=2{(a1+2a1+3a1+…+na1)+[1*2+2*3+3*4+…(n-1)n]d}/n(n+1)=2{(n(n+1)a1/2)+[1*2+2*3+3*4+…(n-1)n]d}/n(n+1)={(n(n+1)a1)+2[1*2+2*3+3*4+…(n-1)n...

千问 · 2011-9-30 17:34:56

数列｛an｝是正项等差数列，若bn＝(a1+2a2+3a3+…+nan)/(1＋2＋3＋…+n)，则数列｛bn｝也为等差数列?设an公差为d，则bn=(a1+2a2+3a3+…+nan)/(1+2+3+…+n)=2(a1+2a2+3a3+…+nan)/n(n+1)=2(a1+2(a1+d)+3(a1+2d)+…+n(a1+(n...

千问 · 2011-9-30 17:34:56

设an=kn+t，则nan=kn^2+tnbn=k(1^2+2^2+....+n^2)+t(1+2+3+...+n)=kn(n+1)(2n+1)/6+tn(n+1)/2...

千问 · 2011-9-30 17:34:56

bn=a1+2(a1+d)+3(a1+2d)+...+n(a1+(n-1)d)
=a1(1+2+3+...+n)+d(2+3*2+4*3+5*4+...+n(n-1))
=a1n(n+1)/2+dn(n+1)(n-1)/3...