src/HOL/Analysis/Harmonic_Numbers.thy
changeset 69064 5840724b1d71
parent 68643 3db6c9338ec1
child 69597 ff784d5a5bfb
     1.1 --- a/src/HOL/Analysis/Harmonic_Numbers.thy	Sun Sep 23 21:49:31 2018 +0200
     1.2 +++ b/src/HOL/Analysis/Harmonic_Numbers.thy	Mon Sep 24 14:30:09 2018 +0200
     1.3 @@ -225,7 +225,7 @@
     1.4      by (intro summable_Leibniz(1) decseq_imp_monoseq decseq_SucI) simp_all
     1.5    hence A: "(\<lambda>n. \<Sum>k<n. (-1)^k / real_of_nat (Suc k)) \<longlonglongrightarrow> (\<Sum>k. (-1)^k / real_of_nat (Suc k))"
     1.6      by (simp add: summable_sums_iff divide_inverse sums_def)
     1.7 -  from filterlim_compose[OF this filterlim_subseq[of "( * ) (2::nat)"]]
     1.8 +  from filterlim_compose[OF this filterlim_subseq[of "(*) (2::nat)"]]
     1.9      have "(\<lambda>n. \<Sum>k<2*n. (-1)^k / real_of_nat (Suc k)) \<longlonglongrightarrow> (\<Sum>k. (-1)^k / real_of_nat (Suc k))"
    1.10      by (simp add: strict_mono_def)
    1.11    ultimately have "(\<Sum>k. (- 1) ^ k / real_of_nat (Suc k)) = ln 2" by (intro LIMSEQ_unique)