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## Homework Statement

Show that if [itex] x_n [/itex] is a convergent sequence, then the sequence given by that average values also converges to the same limit.

[itex] y_n=\frac{x_1+x_2+x_3+.......x_n}{n} [/itex]

## The Attempt at a Solution

Should I say that [itex] x_n [/itex] converges to some number P. so now I need to show that

[itex] y_n [/itex] converges to P as well.

Do I need to show that [itex] y_n-P< \epsilon [/itex]