- #1

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- Homework Statement
- Main body

- Relevant Equations
- Main body

Let ## v_N = \sup \{ s_n : n \gt N \}##. If ## lim \sup s_n = \lim v_N = L##, then for ## \epsilon /gt 0##, we have ##N## such that

$$

m \gt N \implies v_m \lt L + \varepsilon$$

$$

n\gt m \implies s_n \lt L + \epsilon$$

Therefore, ## \lim s_n = L##.

I don't very much understand limit superior, but simply writing it as ##v_N## allowed me to carry out the usual procedure.

$$

m \gt N \implies v_m \lt L + \varepsilon$$

$$

n\gt m \implies s_n \lt L + \epsilon$$

Therefore, ## \lim s_n = L##.

I don't very much understand limit superior, but simply writing it as ##v_N## allowed me to carry out the usual procedure.