What is a Telescoping Series and How Can It Help Solve This Calculus Problem?

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A telescoping series is a type of series where most terms cancel out when summed, simplifying the calculation of the total. In the discussed calculus problem, recognizing the structure of the series can lead to an easier solution. The hint provided suggests that the series in the problem resembles a telescoping series, which can help in finding the answer. Understanding how to manipulate the series to reveal its telescoping nature is key to solving the problem. Ultimately, applying the concept of telescoping series can lead to the correct answer of 2.
Frillth
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I got the following problem for my Calculus course:

http://img291.imageshack.us/img291/7449/problemsw3.jpg

I know the answer to this is 2, but I can't seem to make any headway in this problem. Can somebody give me a hint?
 
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Do you know what a telescoping series is? It looks like that series is pretty close to one.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
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