In mathematics, a telescoping series is a series whose partial sums eventually only have a fixed number of terms after cancellation. The cancellation technique, with part of each term cancelling with part of the next term, is known as the method of differences.
![\sum_{i=1}^n(a_i-a_{i+1}) = (a_1-a_2)+(a_2-a_3)+\ldots+(a_n-a_{n+1})=a_1-a_{n+1}.](/Images/godic/202502/15/419aea04b8d4814ca154dafc2ad73b912348.png")
![\prod_{i=1}^n \frac{a_i}{a_{i+1}} = \frac{a_1}{a_{n+1}}](/Images/godic/202502/15/5ba4295241cf1f35360ec51847c1729a2348.png")