已知数列an满足a1=2,an=a(n-1)+2n,(n≥2),求an
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已知数列an满足a1=2,an=a(n-1)+2n,(n≥2),求an已知数列an满足a1=2,an=a(n-1)+2n,(n≥2),求an已知数列an满足a1=2,an=a(n-1)+2n,(n≥2
已知数列an满足a1=2,an=a(n-1)+2n,(n≥2),求an
已知数列an满足a1=2,an=a(n-1)+2n,(n≥2),求an
已知数列an满足a1=2,an=a(n-1)+2n,(n≥2),求an
原式=an-a(n-1)=2n
a2-a1=2×2
a3-a2=2×3
.
an-a(n-1)=2n
以上各式相加
an-a1=4+6+……+2n=(2n+4)(n-1)÷2=(n+2)(n-1)
所以an=(n+2)(n-1)+2=n²+n
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