Question

Determine whether each sequence below converges or diverges. If the sequence converges, find its limit. Carefully show your work! (a) a_n = sqrt[n]{7^{1+2n}} (b) b_n = frac{(ln n)^3}{n} (c) c_n = frac{n!}{e^n} (d) d_n = (1 + frac{2}{n})^{3n} (e) e_n = frac{sqrt{3+9n^4}}{3n^2+4} (f) f_n = frac{sin 2n}{1+sqrt{n}}

          Determine whether each sequence below converges or diverges. If the sequence converges, find its limit. Carefully show your work!

(a) a_n = sqrt[n]{7^{1+2n}}
(b) b_n = frac{(ln n)^3}{n}
(c) c_n = frac{n!}{e^n}
(d) d_n = (1 + frac{2}{n})^{3n}
(e) e_n = frac{sqrt{3+9n^4}}{3n^2+4}
(f) f_n = frac{sin 2n}{1+sqrt{n}}

$Determine whether each sequence below converges or diverges. If the sequence converges, find its limit. Carefully show your work! (a) an = sqrt[n]7^1+2n (b) bn = frac(ln n)^3n (c) cn = fracn!e^n (d) dn = (1 + frac2n)^3n (e) en = fracsqrt3+9n^43n^2+4 (f) fn = fracsin 2n1+sqrtn$