Theory Arithmetic_Series_Complex

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theory Arithmetic_Series_Complex
imports Complex_Main

(*  Title:      HOL/ex/Arithmetic_Series_Complex
Author: Benjamin Porter, 2006
*)



header {* Arithmetic Series for Reals *}

theory Arithmetic_Series_Complex
imports Complex_Main
begin


lemma arith_series_real:
"(2::real) * (∑i∈{..<n}. a + of_nat i * d) =
of_nat n * (a + (a + of_nat(n - 1)*d))"

proof -
have
"((1::real) + 1) * (∑i∈{..<n}. a + of_nat(i)*d) =
of_nat(n) * (a + (a + of_nat(n - 1)*d))"

by (rule arith_series_general)
thus ?thesis by simp
qed

end