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Homework Statement
Ideal rubber stirng with length L=1km.Ant is takng a walk on the string with speed v=1cm/s
After every minute(Δt=60s) ,string is getting longer by ΔL=1km.
1)Will ant get to the end of string?
2)If yes,then how long it will take ?
Homework Equations
1) So i used series expansion
[itex]\frac{s}{l}[/itex]=[itex]\frac{vΔt}{L}[/itex]+[itex]\frac{vΔt}{L+ΔL}[/itex]+..=
vΔt∑[itex]\frac{1}{L+iΔL}[/itex]
The ant will get to the end when s/l=1
So i got that.
2)But I have problem figuring out how to get the time needed to get there.
I have tip to use integral test,but i do not understand how to use it,beacuse as far as i know,tests are used to test if series converges.
Please,help here ?