..wondering at the world of maths...

[abcde]

AOA!
There are two points 5 cm apart. A string of 1.5 cm is placed at one point in the direction of the other point. In the first hour, the string is extended by 0.05 cm so that its length becomes 1.55 cm. In the second hour, it is extended by 0.005 cm, becoming 1.555 cm. It keeps on extending like this, 1.5555, then 1.55555, then 1.555555 and so on. The dilemma is that even though, it is extending , will it ever reach the other point? Why or why not?
Detailed explanation required please.

 

[Nibz]

Ammm Tricky :| but yes, it'l reach the other point.. because it's been stretched. (thats the possible explanation with me at this time ) Will look at it again, I.A

 

[abcde]

yes common sense suggests that anything whose length is increasing will eventually reach its destination. but the thing thats bugging me is : HOW in this case?

 

[Nibz]

and probably, the number becomes infinite (1.55~) so it won't reach the other point. This can also be a possible solution.

Or wait....
This solution: the 1.5555....6 would become 2 at some point.. then the 2.5555555555555556 (rounding it off) becoming 3 and .. so eventually, the string will touch the other point.

 

[abcde]

that's the thing! it isn't becoming 2... it doesn't ever seem to become 2! you see, the number is only increasing in 'decimals of fives'.

 

[XPFMember]

Assalamoalaikum!!
well..i dont have any explanation...atleast now i dont get to explain it properly!.but it wont reach the other end...

may be bcoz the increase in length is less than one and it keeps decreasing..and may be after som time it'll almost be equal to zero!

 

[Nibz]

^Another Possibility!