数列an满足a1+2a2+3a3+...+nan=(n+1)(n+2) 求通项an
急,看清楚再回答,等号右边是(n+1)(n+2)
人气：142 ℃ 时间：2019-12-19 15:02:27
解答
∵数列{a[n]}满足a[1]+2a[2]+3a[3]+...+na[n]=(n+1)(n+2)∴a[1]+2a[2]+3a[3]+...+na[n]+(n+1)a[n+1]=(n+2)(n+3)将上面两式相减,得：(n+1)a[n+1]=2(n+2)∴a[n+1]=2(n+2)/(n+1) 即：a[n]=2(n+1)/n (n≥2)∵a[1]=(n+1)(...
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