Question

已知数列an中,a1=1,an=an-1+1/n（n-1）,则an的通项公式是?

Answer 1

观察证法：原式变亮缺换 an - an-1=1/n(n-1) =-[1/n - 1/(n-1)]
观察可知an=-1/n
保守证孙键裤法：
a2-a1 = -(1/2 - 1)
a3-a2 = -(1/3 - 1/2)
a4-a3 = -(1/4 - 1/3)
...
a(n-1)-a(n-2)=-[1/(n-1) - 1/(n-2)]
an - an-1=1/n(n-1) =-[1/n - 1/(n-1)]
将左右全部相加得an - a1 = -(-1+1/n) a1=1代入
an=1+1-1/n = -1/n
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