The sequence

{a_(n)}

is defined by

a_(1)=2

, and\

a_(n+1)=(1)/(2)(a_(n)+(2)/(a_(n)))

\ for

n>=1

. Assuming that

{a_(n)}

converges, find its limit.\

\\\\lim_(n->\\\\infty )a_(n)=

\ Hint: Let

a=\\\\lim_(n->\\\\infty )a_(n)

. Then, since

a_(n+1)=(1)/(2)(a_(n)+(2)/(a_(n)))

, we have

a=(1)/(2)(a+(2)/(a))

. Now solve for

a

.

The sequence {an} is defined by a1=2, and an+1=21(an+an2) for n1. Assuming that {an} converges, find its limit. limnan= Hint: Let a=limnan. Then, since an+1=21(an+2/an), we have a=21(a+2/a). Now solve for a. The sequence {an} is defined by a1=2, and an+1=21(an+an2) for n1. Assuming that {an} converges, find its limit. limnan= Hint: Let a=limnan. Then, since an+1=21(an+2/an), we have a=21(a+2/a). Now solve for a