已知數(shù)列{an}滿足a1=4,an=4-4/(an-1)(n大于等于2)求數(shù)列an的通項(xiàng)公式.

熱心網(wǎng)友

an=4-4/(an-1)(n大于等于2)an=[4(an-1)-4]/(an-1)an-2=[4(an-1)-4]/(an-1)-2=2*[(an-1)-2]/(an-1)1/(an-2)=(an-1)/{2*[(an-1)-2]}=1/2+1/[(an-1)-2]設(shè){bn}={1/(an-2)},則bn是等差函數(shù)。公差是1/2求得bn=1/2*(n-1)+b1,b1=1/(a1-2)=1/2,bn=n/2帶入{bn}={1/(an-2)}式中即可得an=2+2/n

熱心網(wǎng)友

an=4-4/(an-1)(n大于等于2)an=[4(an-1)-4]/(an-1)an-2=[4(an-1)-4]/(an-1)-2=2*[(an-1)-2]/(an-1)1/(an-2)=(an-1)/{2*[(an-1)-2]}=1/2+1/[(an-1)-2]設(shè){bn}={1/(an-2)},則bn是等差函數(shù)。公差是1/2求得bn=1/2*(n-1)+b1,b1=1/(a1-2)=1/2,bn=n/2帶入{bn}={1/(an-2)}式中即可得an=2+2/n