Answer to Question #82678 in Real Analysis for Zaighum abbas

Question

Qno.1) a) check whether the following sequences are cauchy sequence or not ?
I) (n+1/n) ii) (1+1/2!+.....+1/n!)
iii) (-1)^n iv) (n+ (-1)^n/n)
b) let x1<x2 be arbitrary real number and Xn= 1/2(Xn-2+Xn-1) for n>2. Show that (Xn) is convergent ? What is it limit ?