设曲线y=x^n^2+n在点(1,1)处的切线与x轴的交点的横坐标为xn,则数列{xn}前10项和等于 20
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y = x^(n^2+n)
y' = (n^2+n )x^(n^2+n-1)
y'(1)= n^2+n
点(1,1)处的切线
y-1 = (n^2+n)(x-1)
y=0, x=xn
-1 =(n^2+n)(xn-1)
xn = (n^2+n-1)/(n^2+n)
= 1- 1/(n^2+n)
= 1- [ 1/n - 1/(n+1) ]
S10 = 10-[1 - 1/11]
= 100/11
Ans: A
y' = (n^2+n )x^(n^2+n-1)
y'(1)= n^2+n
点(1,1)处的切线
y-1 = (n^2+n)(x-1)
y=0, x=xn
-1 =(n^2+n)(xn-1)
xn = (n^2+n-1)/(n^2+n)
= 1- 1/(n^2+n)
= 1- [ 1/n - 1/(n+1) ]
S10 = 10-[1 - 1/11]
= 100/11
Ans: A
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