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