数列an满足a1+2a2+3a3+...+nan=(n+1)(n+2) 求通项an

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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)

∵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)(n+2)=(1+1)(1+2)=6
而a[1]=2(n+1)/n=2(1+1)/1=4
两者不一致
∴通项a[n]=1 (n＝1)
a[n]=2(n+1)/n (n≥2)

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