ABSTRACT
An infinite sequence is a list a 1, a 2, a 3, . . . of real numbers, indexed by the positive integers. Here are some examples: a 1 , a 2 , a 3 , a 4 , … , a 42 , … = 1 , 1 2 , 1 3 , 1 4 , … , 1 100 , … ; $$ a_{1} ,\,\,\,a_{2} ,\,\,a_{3} ,\,\,a_{4} , \ldots ,\,a_{{42}} ,\, \ldots \,\,\,\, = \,\,\,1,\,\,\,\frac{1}{2},\,\,\frac{1}{3},\,\,\,\frac{1}{4},\, \ldots ,\frac{1}{{100}},\, \ldots ; $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315315089/a42df629-db93-4a2b-bdb7-991074d3ccb1/content/math2_1.tif"/> b 1 , b 2 , b 3 , b 4 , … , b 42 , … , = 1 , - 1 , 1 , - 1 , … , - 1 … , ; $$ b_{1} ,\,\,b_{2} ,\,\,b_{3} ,\,\,b_{4} ,\, \ldots ,b_{{42}} ,\, \ldots ,\,\, = \,\,1,\, - 1,\,1, - 1, \ldots , - 1 \ldots ,; $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315315089/a42df629-db93-4a2b-bdb7-991074d3ccb1/content/math2_2.tif"/> c 1 , c 2 , c 3 , c 4 … , c 42 , … = sin 1 , sin 2 , sin 3 , sin 4 , … sin 42 , … ; $$ c_{1} ,\,\,\,c_{2} ,\,\,\,c_{3} ,\,\,c_{4} \ldots ,\,c_{{42}} , \ldots \,\, = \,\,\sin 1,\,\sin 2,\,\,\sin 3,\,\,\sin 4, \ldots \sin 42, \ldots ; $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315315089/a42df629-db93-4a2b-bdb7-991074d3ccb1/content/math2_3.tif"/> f 1 , f 2 , f 3 , f 4 , … , f 42 , … = 1 , 1 , 2 , 3 , … , 267914296 , … ; $$ f_{1} ,\,\,\,f_{2} ,\,\,f_{3} ,\,\,f_{4} ,\, \ldots ,f_{{42}} , \ldots \,\,\, = \,\,1,1,2,3, \ldots ,267914296, \ldots ; $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315315089/a42df629-db93-4a2b-bdb7-991074d3ccb1/content/math2_4.tif"/> g 1 , g 2 , g 3 , g 4 , … , g 42 , … = 1 1 , 2 1 , 3 2 , 5 3 , … , 433494437 267914296 , … $$ g_{1} ,\,\,g_{2} ,\,g_{3} ,\,g_{4} ,\, \ldots ,g_{{42}} , \ldots \,\,\, = \,\,\frac{1}{1},\frac{2}{1},\frac{3}{2},\frac{5}{3}, \ldots ,\frac{{433494437}}{{267914296}}, \ldots $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315315089/a42df629-db93-4a2b-bdb7-991074d3ccb1/content/math2_5.tif"/>
