Sentence examples for be a convergent sequence from inspiring English sources

Let be a convergent sequence in.

(1) Let be a convergent sequence in.

Let be a convergent sequence in and as.

Let ({x_{k}}) be a convergent sequence in ((X, A)).

Let { v n } be a convergent sequence in C and v n → v as n → + ∞.

Let { ω n } be a convergent sequence in W and ω n → ω, as n → + ∞.

Therefore, the Cauchy sequence ({y_{n}}) is a convergent sequence, and it converges to a point z (say) in X.

This completes the proof that F ( T ) ⊂ C n. Next, we show that { x n } is a convergent sequence which strongly converges to x ¯, where x ¯ ∈ F ( T ).

In order to show that the functions are a convergent sequence, we use the Cauchy convergence criterion.

Since ( X, q ) is right-convergent, then { T g x n } is a convergent sequence in ( X, q ), and by item 4 of Remark 2.3, it converges to Tu. □.

Therefore, is a convergent sequence.