Question: how to find the formula for the nth partial sum?
Answer: The nth partial sum of this series is sn = ( 1 - 1 2 ) + (1 2 - 1 3 ) + (1 3 - 1 4 ) + (1 4 - 1 5 ) + ··· + (1 n - 1 n + 1 ) = 1 - 1 n + 1 . sn = 1, the series converges with sum 1. arn = a + ar + ar2 + ar3 + ··· , where a is a constant and r is called the ratio of the series.