5-21 数列前N项和公式

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,数列前,N,项和,4.,设函数,f,(,x,)=log,2,x,-,log,x,2(0,x,1),数列,a,n,满足,f,(2,a,n,)=2,n,n,=1,2,3,.(1),求数列,a,n,的通项公式,;(2),判断数列,a,n,的单调性,.,4.,设函数,f,(,x,)=log,2,x,-,log,x,2(0,x,1),数列,a,n,满足,f,(2,a,n,)=2,n,n,=1,2,3,.(1),求数列,a,n,的通项公式,;(2),判断数列,a,n,的单调性,.,解,:,(1),由已知,log,2,2,a,n,-,=2,n,log,2,2,a,n,1,a,n,-,=2,n,1,a,n,即,a,n,2,-,2,na,n,-,1=0.,解得,a,n,=,n,n,2,+1.,故,a,n,=,n,-,n,2,+1(,n,N,*,).,0,x,1,即,02,a,n,1,a,n,0.,(2),=,a,n,+1,a,n,(,n,+1),-,(,n,+1),2,+1,n,-,n,2,+1,(,n,+1)+,(,n,+1),2,+1,n,+,n,2,+1,=,1.,而,a,n,a,n,.,故,数列,a,n,是递增数列,.,8.,已知数列,a,n,b,n,满足,a,1,=1,a,2,=,a,(,a,为常数,),且,b,n,=,a,n,a,n,+1,其中,n,=1,2,3,.,(1),若,a,n,是等比数列,试求数列,b,n,的前,n,项和,S,n,的公式,.,8.,已知数列,a,n,b,n,满足,a,1,=1,a,2,=,a,(,a,为常数,),且,b,n,=,a,n,a,n,+1,其中,n,=1,2,3,.,(1),若,a,n,是等比数列,试求数列,b,n,的前,n,项和,S,n,的公式,.,解,:,a,n,是等比数列,a,1,=1,a,2,=,a,a,0,a,n,=,a,n,-,1,.,又,b,n,=,a,n,a,n,+1,b,1,=,a,1,a,2,=,a,且有,:,b,n,+1,b,n,a,n,a,n,+1,a,n,+1,a,n,+2,=,a,2,.,a,n,+2,a,n,b,n,是以,a,为首项,a,2,为公比的等比数列,.,当,a,=1,时,S,n,=1+1+,+1=,n,;,当,a,=,-,1,时,S,n,=,-,1,-,1,-,-,1=,-,n,;,当,a,1,时,S,n,=,.,1,-,a,2,a,(1,-,a,2,n,),1,-,a,2,a,(1,-,a,2,n,),故,S,n,=,n,a,=1,-,n,a,=,-,1,a,1.,