Question

Determine whether the sequence is increasing, decreasing, or not monotonic.

Answer 1

\[a_n = 5n + \frac{ 1 }{ n }\]

Answer 2

It's increasing is it not?

Take the limit, 5n goes to infinity, but 1/n goes to zero

so we get lim n -> infinity = infinity + 0 which is infinity.

Answer 3

1/n = infinity= zero..... 5n= infinity?

Answer 4

ok

Answer 5

so, this means increasing but not bounded?

Answer 6

Yeah there is no bound on it.

Answer 7

Think of it as just a linear function, y = n

Answer 8

Because the 1/n becomes irrelevant as n approaches infinity.