Question

lim(n→∞) 1/(n+1)-2/(n+1)+3/(n+1)-4/(n+1)+...+[(2n-1)/(n+1)]-[(2n)/(n-1)]求极限

Answer 1

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

Answer 2

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