设b＞0,数列an满足a1=b,an=nban-1/an-1+n-1（n≥2）求数列an通向公式._其他解答

设b＞0,数列an满足a1=b,an=nban-1/an-1+n-1（n≥2）求数列an通向公式.

人气：327 ℃　时间：2019-08-18 15:35:59

解答

an=nba(n-1)/(a(n-1)+n-1)an.a(n-1) +(n-1)an = nba(n-1)1+(n-1)[ 1/a(n-1)] = nb (1/an)(n-1)( 1/a(n-1) +[1/(1-b)]/(n-1)) = nb( 1/an + [1/(1-b)]/n )( 1/an + [1/(1-b)]/n ) /( 1/a(n-1) +[1/(1-b)]/(n-1)) = (1...