Tests of convergence (comparison, ratio, root, integral)
General · Mathematics
Study notes
Q: Test Σn!/nⁿ and Σ1/(n²+1) for convergence. Σn!/nⁿ: ratio: (n+1)!/(n+1)ⁿ⁺¹ × nⁿ/n! = nⁿ/(n+1)ⁿ = 1/(1+1/n)ⁿ → 1/e < 1: CONVERGES! Σ1/(n²+1): 1/(n²+1) < 1/n², Σ1/n² converges: CONVERGES (comparison!)!