ABSTRACT
The binomial series or binomial theorem is a formula for raising a binomial expression to any power without lengthy multiplication. ( a + x) n = a n + na n − 1 x + n ( n − 1 ) 2 ! a n − 2 x 2 + n ( n − 1 ) ( n − 2 ) 3 ! a n − 3 x 3 + ⋯ ⋯ + x n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq1141.tif"/> ( 1 + x) n = 1 + nx + n ( n − 1 ) 2 ! x 2 + n ( n − 1 ) ( n − 2 ) 3 ! x 3 + ⋯ ⋯ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq1142.tif"/>
