AMC 8 2022 (Problem 8)What is the value of 13⋅24⋅35⋯1820⋅1921⋅2022\frac{1}{3}\cdot\frac{2}{4}\cdot\frac{3}{5}\cdots\frac{18}{20}\cdot\frac{19}{21}\cdot\frac{20}{22}31⋅42⋅53⋯2018⋅2119⋅2220?(A) 1462\text{(A)}\;\frac{1}{462}(A)4621(B) 1231\text{(B)}\;\frac{1}{231}(B)2311(C) 1132\text{(C)}\;\frac{1}{132}(C)1321(D) 2213\text{(D)}\;\frac{2}{213}(D)2132(E) 122\text{(E)}\;\frac{1}{22}(E)221Related TopicsToolkit 5 — Telescoping seriesHints (1)Hint 1Use Identity 5. Telescoping Series.Final Answer(E) 122\frac{1}{22}221