⊢ ¬Summable fun i => 1 / (↑i + 1)


⊢ ∀ (n : ℕ), 0 ≤ 1 / (↑n + 1)
⊢ Tendsto (fun n => ∑ i in Finset.range n, 1 / (↑i + 1)) atTop atTop
rw [← not_summable_iff_tendsto_nat_atTop_of_nonneg]
no goals
⊢ ¬Summable fun i => 1 / (↑i + 1)
exact_mod_cast mt (_root_.summable_nat_add_iff 1).1 Real.not_summable_one_div_nat_cast
no goals
⊢ ∀ (n : ℕ), 0 ≤ 1 / (↑n + 1)
exact fun i => div_nonneg zero_le_one i.cast_add_one_pos.le