Bug rope climbing problem

Analysis: The worm climbs 1 cm per second, and after each 1 cm climb, the rope is elongated by 1 m = 100 cm

1st second: the worm climbed 1cm, the rope was 100cm long, and the worm climbed the rope in 1 second with a total length of 1 100; The bugs climbed a total of 1,100 meters.

Second 2: The worm climbed 1cm, the rope is 200cm long, and the worm climbs the rope in this second with a total length of 1 200; The bugs climbed a total of 1 100 + 1 200 meters.

The third second: the worm climbed 1cm, the rope is 300cm long, and the worm climbs the rope in this second The total length of the rope is 1 300; The worms climbed a total of 1 100 + 1 200 + 1 300 meters.

The nth second: the worm climbed 1cm, the rope length n*100cm, the worm climbed the rope length of 1 n*100 in the second; The worms crawled a total of 1 100 + 1 200 + 1 300 +...1 n*100 meters.

After n seconds, the worm crawls to the right, and n is satisfied with the condition:

1/100+1/200+1/300+..1/n*100=1

1+1/2+1/3+1/4+1/5+..1/n=100

Obviously 1+1 2+1 3+1 4+1 5+...1 n is a divergent sequence when n approaches infinity.

i.e.: n-->, 1+1 2+1 3+1 4+1 5+...1/n =∞

So n has a solution.

Solution: 1+1 2+1 3+1 4+1 5+...1/n=100

Set: 1+1 2+1 3+1 4+...1/n=s(n)

When n approaches infinity.

n s(n)=lim ∑(1/i)

n->∞i=1

n lim ∑(1/n)*(n/i)

n->∞i=1

dx x because dx x = ln(x).

1+1/2+1/3+1/4+..When 1 n=s(n)=100, s(n) is the area of the graph enclosed by the line 1 x=y, the line x=1 and the line x=1 n in the Cartesian coordinate system.

i.e.: s(n) = dx x = ln(1)-ln(1 n) = -ln(1 n) = ln(n) = 100

1/nn=e^100

So the final answer is: after 100 seconds of e, the worm crawls to the right side of the rope.

What kind of rope are you 1m 1 second stretching 1m a minute is 60m Do you think the worm can climb up Although the distance that the worm crawls is increasing, the distance at the other end of the rope is also increasing dramatically The person who came up with this problem has a very bad brain.

The bug cannot climb to the other end of the rope.

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