What is Telescoping Sum?
Telescoping sum is one of very useful summation properties. Telescoping sum simplify our summation because it says that sum of a difference is equal to the last and first term only, not depending on the middle terms.
Suppose we have a sequence of numbers then we can put index on the sequence such that , , , , , and we want to compute the sum of difference
Preferable reference for this tutorial is
Teknomo, Kardi (2015) Summation Tutorial. http://people.revoledu.com/kardi/tutorial/BasicMath/Sum/