worm on an elastic band

dont [17][17][17].......be [1][1][1]...celestine........[9][9][9]...............

Please tell me if I am making a mistake.

The distance moved by worm in 1 day = 1inch
String length after 1 day = 30 inches
This increases distance betwwen any two points on string increases to 30/20 times original.
So distance moved by worm in 1st day is 3/2 inches.

So the following algorithm can be made

(d_(n-1) + 1) (n+2) / (n+1) = d_n where d_n denotes distance moved by the nth day.

How do I solve this.

Ans is COOL[4]

[e¹⁰]=22026 days

assume:worm has a life of more than 60 years!!!![3]

hint
ans comes in exponential terms

try forming a integrable eq

bhaiya...is this physics or mathematics....[12]

then i ve done a mistake putting it here[3]

Is the time taken 98 days?

Initially the worm is at one end of the string. In one day it moves 1 inch. Then the boy increases the length to 30 inches.

That is he increases distance between 2 points on the string to 3/2 times original distance.

Then Distance moved by worm is 3/2 inches. After 1 more day, the distance moved becomes (3/2 + 1) = 5/2 inches. Then the boy increases length to 40 inches.

Effectively increasing distance between 2 points to 4/3 times original. Now the worm has moved (4/3)(5/2) = 10/3 inches.
Percentage distance moved by worm in 1st day = {(3/2)/30 } 100 = 5%
percentage distance moved in 2nd day = {(10/3)/40} 100 = 8.33%
percentage distance moved in 3nd day = 10.83%
It is increasing therefore sometime it must become 100% Trying out the time taken now.

Do we assume that the elastic band will not break . (There are some stupid riddles which have such answers )

this can be a hint : (had it saved in mah pc..)

Elastic Materials can regain itz original configuration after it is streched...so definitely the worm will reach the other end.........