lim[(2n-1)an]=2,求limnan
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lim[(2n-1)an]=2,求limnan
![lim[(2n-1)an]=2,求limnan](/uploads/image/z/1794260-20-0.jpg?t=lim%5B%282n-1%29an%5D%3D2%2C%E6%B1%82limnan)
这是数列极限,an中的n应该是下标吧,莪用(an)表示之.
lim(n->∞) n(an)
=lim(n->∞) [n/(2n-1)]*[(2n-1)*(an)]
=lim(n->∞) n/(2n-1) * lim(n->∞) (2n-1)*(an)
=lim(n->∞) 1/(2-1/n) * lim(n->∞) (2n-1)*(an)
=1/(2-0) * 2
=1
lim(n->∞) n(an)
=lim(n->∞) [n/(2n-1)]*[(2n-1)*(an)]
=lim(n->∞) n/(2n-1) * lim(n->∞) (2n-1)*(an)
=lim(n->∞) 1/(2-1/n) * lim(n->∞) (2n-1)*(an)
=1/(2-0) * 2
=1
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