Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises - Page 605: 45

Converges to $1$

$a_n = \frac{5^n}{5^n + 1}$ $a_1 = 0.833333$ $a_2 = 0.961538$ $a_3 = 0.992063$ $a_4 = 0.998403$ $a_5 = 0.99968$ $a_6 = 0.999936$ $a_7 = 0.999987$ $a_8 = 0.999997$ $a_9 = 0.999999$ $a_{10} = 1.00000$ The terms of the sequence seems to get closer to $1$ as $n$ increases.