#### extrazlove

##### New member

- Joined
- Feb 15, 2019

- Messages
- 8

Here is a Z

_{n }Suite

Z

_{3}= 1/2

Z

_{n}= Z

_{n+1}/ \cos (pi / n)

It's a bizarre suite decreasing to 0 without ever going.

I will define the n with which I work in my suite so as not to fall into absurdities like 1/0 which gives false calculations.

find that

n = pi / arccos (Z

_{n+1}/ Z

_{n})

Note that Z

_{n}#0 and Z

_{n+1}/ Z

_{n}#1

so the Z

_{n+1 }limit is non-zero.

And since I have a decreasing sequence, Z

_{n+1}/ Z

_{n}< 1, so the series Z

_{n}is convergent according to the d'Alembert criterion.

Is there an error in this reasoning?

Z

_{n}is a positive term and is decreasing and minus 0 tends to 0 minus bound 0, which is impossible because Z

_{n }#0?