8. Identify which of the following sequences are Cauchy sequences and hence must converge, even in cases where their limiting values may be unknown.

(a) dn ¼ n nþ1

(b) xn ¼ 2n24 4n2þ10

(c) yn ¼

Pn j¼1ð1Þ jþ1

(d) xn ¼

Pn j¼1ð1Þ jþ12j

(e) fn ¼

Pn j¼1ð1Þ jþ1aj , a > 1

(f ) ck ¼ k þ 1 k