azebweyessa
azebweyessa azebweyessa
  • 12-02-2021
  • Mathematics
contestada

What is the upper bound for n/(2n+1)​

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963tygpw58
963tygpw58 963tygpw58
  • 12-02-2021
You need a bit more. That the limit of the sequence is 2
2
isn't enough. You also need, that this sequence is monotonous. Then you can say that 2
2
is the upper bound.

You can try it this way:

As
n
approaches infinity, you see that
n
gets much bigger than 1, so you can neglect it and you get
lim→∞21+=lim→∞2=2.
lim
n
→
∞
2
n
1
+
n
=
lim
n
→
∞
2
n
n
=
2.

Because
a
n
is monotonous, you see, that this is indeed the upper bound.
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