Find the sum of the series :
The traditional way to solve this probelm is compute the individual values for each of the fractions and then add the results. That is,
At best, this is a rather laborious task and is likely to lead to some error. Let’s see if we can find some kind of pattern we can use:
The pattern that emerges strongly suggest that the sum of this series, with its last term 1/49+50, will be 49/50. Here the finding a pattern strategy was a bit hidden in the problem.
Another application of recognizing a pattern to help us a solution can be seen if we consider these fraction as
We seek the sum of the left side, wich is equal to the sum of the right side, where every term drops out except for the first and the last terms :