Question

(1/2)已知A1=An+1=An+2n,求An累加法。An=2(n-1)还是1+n(n+1)?我看不懂An-A1=2+2×2+2×3+--+2

(1/2)已知A1=An+1=An+2n,求An累加法。An=2(n-1)还是1+n(n+1)?我看不懂An-A1=2+2×2+2×3+--+2(2/2)(n-1)?不是An=A1+2(2+--+n)吗？括号内求和Sn?

Answer 1

n≥2
A2-A1=2
A3-A2=4
A4-A3=6
..............
An-A(n-1)=2(n-1)
累加得：
An-A1=2+4+6+....+2(n-1)
=(2+2n-2)*(n-1)/2=n(n-1)
An=A1+n(n-1)
n=1上式也适合
∴An=A1+n(n-1)