lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n-1)]求极限
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![lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n-1)]求极限](/uploads/image/z/3937661-53-1.jpg?t=lim%28n%E2%86%92%E2%88%9E%29+1%2F%28n%2B1%29-2%2F%28n%2B1%29%2B3%2F%28n%2B1%29-4%2F%28n%2B1%29%2B...%2B%5B%282n-1%29%2F%28n%2B1%29%5D-%5B%282n%29%2F%28n-1%29%5D%E6%B1%82%E6%9E%81%E9%99%90)
lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n-1)]求极限
lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n-1)]求极限
lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n-1)]求极限
lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n-1)]
=lim(n→∞) (-1)*n/(n+1)
=lim(n→∞) [-1/(1+1/n)]
=-1
lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n-1)] 牛最后面的(n-1)是不是写错了,应该是(n+1)吧。
lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n+1)]
=lim(n→∞) -n/(n+1...
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lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n-1)] 牛最后面的(n-1)是不是写错了,应该是(n+1)吧。
lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n+1)]
=lim(n→∞) -n/(n+1)
=lim(n→∞) -1/(1+1/n)
因为当n趋近于无穷时1/n趋近于0所以=lim(n→∞) -1/(1+1/n)=-1
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