如果一个数列{An}满足A1=2,An+1=An+2n《n为自然数》,那么A100是=?
来源:百度知道 编辑:UC知道 时间:2024/05/31 05:53:19
A(1) = 2
A(n + 1) = A(n) + 2n
A(1) = 2
A(2) = 2 + 2*1
A(3) = 2+2*1+2*2
A(4) = 2+2*1+2*2+2*3
A(n) = 2+2*[1 + 2 + 3 + ..... + (n-1)]
A(100) = 9902
就是2的100次方
这里采用括号书写下标。
A(1) = 2
A(n + 1) = A(n) + 2n
A(1) = 2 = 2*1
A(2) = 2 + 2*2 = 2*(1 + 2)
A(3) = 2*(1 + 2) + 2* 3 = 2*(1 + 2 +3)
A(4) = 2*(1 + 2 + 3) + 2*4 = 2*(1 + 2 + 3 + 4)
A(n) = 2*(1 + 2 + 3 + ..... + n)
= n(n + 1)
A(100) = 100*101 = 10100
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